1. EJERCICIO 11. Una deuda se expresa en sentido1. Una deuda se expresa en sentido1. Una deuda se expresa en sentido1. Una deuda se expresa en sentido1. Una deuda se expresa en sentidonegativo. Luego inicalmente el estadonegativo. Luego inicalmente el estadonegativo. Luego inicalmente el estadonegativo. Luego inicalmente el estadonegativo. Luego inicalmente el estadoeconmico de Pedro es - 60 bs.econmico de Pedro es - 60 bs.econmico de Pedro es - 60 bs.econmico de Pedro es - 60 bs.econmico de Pedro es - 60 bs.Al recibir 320 bs. Aumenta su capitalAl recibir 320 bs. Aumenta su capitalAl recibir 320 bs. Aumenta su capitalAl recibir 320 bs. Aumenta su capitalAl recibir 320 bs. Aumenta su capitaltantos bs. como ha recibido; entoncestantos bs. como ha recibido; entoncestantos bs. como ha recibido; entoncestantos bs. como ha recibido; entoncestantos bs. como ha recibido; entoncesla operacin queda expresada comola operacin queda expresada comola operacin queda expresada comola operacin queda expresada comola operacin queda expresada comose indicase indicase indicase indicase indica + = +60 320 260 bs.2.2.2.2.2. 1 170 1 515 345. . = sucres3.3.3.3.3. 200 56 189 67+ = + $4.4.4.4.4. + = +665 1 178 2 280 437. . soles5.5.5.5.5. 20 15 40 75 30 + = $6.6.6.6.6. + + = 67 72 16 2 9$7.7.7.7.7. 200 78 81 93 41 59 70 + = colones8.8.8.8.8. + =45 66 79 200 10 0EJERCICIO 21.1.1.1.1. 12 15 3 = !2.2.2.2.2. + = 3 8 6 1!3.3.3.3.3. ( )15 3 15 3 18 = + = !4.4.4.4.4. ( ) + = + =8 5 8 5 13!5.5.5.5.5. + + = 4 7 2 11 6!6.6.6.6.6. + = + = + = + = + = + = + 8 4 1 8 4 4 78 4 2 8 8 0 88 4 5 8 20 12 11!!!amamam7.7.7.7.7. = = = = + = + = + = + = + 1 2 2 1 4 5 101 2 3 1 6 7 111 2 3 3 1 1 6 3 4 121 2 3 3 3 1 6 9 2 2!!!!amamampm8.8.8.8.8. + = 56 7 49!9.9.9.9.9.( ) + = + = 71 5 6615 5 20!!longlat.10.10.10.10.10. 18 3 2165 4 61+ =+- =+!!longlat.11.11.11.11.11. - + =+75 135 60 aosEJERCICIO 31.1.1.1.1. + 32 16m m;2.2.2.2.2. + 10 4m m;3.3.3.3.3. 50 85 35 = m4.4.4.4.4. = 6 11 66m5.5.5.5.5. - =- =+8 6 489 6 54mm6.6.6.6.6. 400 2 800400 3 1 200 = + = m corredorm yo.7. Los 40 pies de longitud del poste7. Los 40 pies de longitud del poste7. Los 40 pies de longitud del poste7. Los 40 pies de longitud del poste7. Los 40 pies de longitud del postese reparten asi: 15 pies que sobresalense reparten asi: 15 pies que sobresalense reparten asi: 15 pies que sobresalense reparten asi: 15 pies que sobresalense reparten asi: 15 pies que sobresalen- se asumen en sentido positivo- .- se asumen en sentido positivo- .- se asumen en sentido positivo- .- se asumen en sentido positivo- .- se asumen en sentido positivo- .25 pies que se encuentran enterrados.25 pies que se encuentran enterrados.25 pies que se encuentran enterrados.25 pies que se encuentran enterrados.25 pies que se encuentran enterrados.- se asumen en sentido negativo - .- se asumen en sentido negativo - .- se asumen en sentido negativo - .- se asumen en sentido negativo - .- se asumen en sentido negativo - .Al introducir 3 pies ms, se adicionanAl introducir 3 pies ms, se adicionanAl introducir 3 pies ms, se adicionanAl introducir 3 pies ms, se adicionanAl introducir 3 pies ms, se adicionana los que estan bajo el suelo y se debena los que estan bajo el suelo y se debena los que estan bajo el suelo y se debena los que estan bajo el suelo y se debena los que estan bajo el suelo y se debendescontar de los que estan por encima.descontar de los que estan por encima.descontar de los que estan por encima.descontar de los que estan por encima.descontar de los que estan por encima.Aritmticamente significa:Aritmticamente significa:Aritmticamente significa:Aritmticamente significa:Aritmticamente significa:40 15 2525 3 2815 3 12= + = + = +piespies8.8.8.8.8. 55 52 3 = + m9.9.9.9.9. + = 32 15 17m10.10.10.10.10. 35 47 12 = m11.11.11.11.11. + = +39 56 17m12.12.12.12.12. 90 58 36 4 = m13.13.13.13.13. 72 30 1 72 30 4272 30 2 72 60 1272 30 3 72 90 1872 30 4 72 120 48 = = + = = + = = = = mmmm14.14.14.14.14. ( )( )( )( ) = + = = + = = + = + = + = +120 60 1 120 60 60120 60 2 120 120 0120 60 3 120 180 60120 60 4 120 240 120KmKmKm

2. EJERCICIO 7.1.1.1.1.1. x x x+ =2 32.2.2.2.2. 8 9 17a a a+ =3.3.3.3.3. 11 9 20b b b+ =4.4.4.4.4. = b b b5 65.5.5.5.5. = 8 9m m m6.6.6.6.6. = 9 7 16m m m7.7.7.7.7. 4 5 9a a ax x x+ =8.8.8.8.8. 6 8 141 1 1a a ax x x+ + ++ =9.9.9.9.9. = + + +m m mx x x1 1 15 610.10.10.10.10. = 3 42 2 2a a ax x x11.11.11.11.11.12121 1222a a a a a+ =+= =12.12.12.12.12.35110610710ab abab abab+ =+=13.13.13.13.13.13162 163612xy xy xy xy xy+ =+= =14.14.14.14.14. = = = 15451 4555xy xy xy xy15.15.15.15.15. = = 561820 32423242 2 2 2a b a b a b a b16.16.16.16.16. = = a a a a788 7815817.17.17.17.17. 8 9 6 23a a a a+ + =18.18.18.18.18. 15 20 36x x x x+ + =19.19.19.19.19. = 7 8 9 24m m m m20.20.20.20.20. = a b a b a b a b2 2 2 23 521.21.21.21.21. a a a ax x x x+ + =3 8 1222.22.22.22.22. = + + + +5 3 5 131 1 1 1a a a ax x x x23.23.23.23.23. a a a a a+ + =+ +=12236 3 4613624.24.24.24.24. = = x x x x x23166 4 1611625.25.25.25.25.153102 3 1010151032ax ax ax ax ax ax+ + =+ += =26.26.26.26.26. = = 34569 10 121231122 2 2 2 2a x a x a x a x a x27.27.27.27.27. 11 8 9 11 39a a a a a+ + + =28.28.28.28.28. m m m m mx x x x x+ + + + ++ + + =1 1 1 1 13 4 6 1429.29.29.29.29. =x y x y x y x y x y2 2 2 2 28 9 20 3830.30.30.30.30. = 3 5 6 9 23a a a a am m m m m31.31.31.31.31.1214184 2 1 88158a a a a a a+ + + =+ + +=32.32.32.32.32.25121101208 10 2 1202120ax ax ax ax ax ax+ + + =+ + +=33.33.33.33.33. 0 5 0 6 0 7 0 8 2 6, , , , ,m m m m m+ + + =34.34.34.34.34. = = = 171141284 2 1 2828352854ab ab ab abab ab ab35.35.35.35.35. = = 23161911224 6 4 33637363 3 3 33 3x y x y x y x yx y x y36.36.36.36.36. ab ab ab ab ab ab2 2 2 2 2 27 9 21 39+ + + + =37.37.37.37.37. = m m m m m m8 7 3 2038.38.38.38.38. = + + + + + +x x x x x xa a a a a a1 1 1 1 1 18 4 5 1939.39.39.39.39.121314151630 20 15 12 106087602920a a a a aa a a+ + + +=+ + + += =40.40.40.40.40. = = 1316121121912 6 18 3 4364336ab ab ab ab abab abEJERCICIO 81.1.1.1.1. 8 6 2a a a =2.2.2.2.2. 6 8 2a a a = 3.3.3.3.3. 9 15 6ab ab ab = 4.4.4.4.4. 15 9 6ab ab ab =5.5.5.5.5. 2 2 0a a =6.6.6.6.6. + =7 7 0b b7.7.7.7.7. + =14 32 18xy xy xy 3. 8.8.8.8.8. + =25 32 72 2 2x y x y x y9.9.9.9.9. 40 51 113 3 3x y x y x y = 10.10.10.10.10. + =m n m n m n2 2 26 511.11.11.11.11. + =15 40 25xy xy xy12.12.12.12.12. 55 81 263 2 3 2 3 2a b a b a b = 13.13.13.13.13. + =x y x y2 2014.14.14.14.14. + =9 9 02 2ab ab15.15.15.15.15. 7 7 02 2x y x y =16.16.16.16.16. + =101 118 17mn mn mn17.17.17.17.17. 502 405 97ab ab ab =18.18.18.18.18. + = 1024 1018 6x x x19.19.19.19.19. + =15 15 0ab ab20.20.20.20.20.12342 3414a a a a == 21.21.21.21.21.34123 2414a a a a ==22.22.22.22.22.5651210 5125122 2 2 2a b a b a b a b ==23.23.23.23.23. + = +=479148 9141142 2 2 2x y x y x y x y24.24.24.24.24.38543 10878am am am am == 25.25.25.25.25. + = += am am am am355 352526.26.26.26.26.567820 2124124mn mn mn mn == 27.27.27.27.27. + = += a b a b a b a b2 2 2 231111 31181128.28.28.28.28. 3 4 5 6 2 24 3 4 3 4 3, , ,a b a b a b = 29.29.29.29.29. + =12 3 4 2 2, , ,yz yz yz30.30.30.30.30. 4 2 2a a ax x x =31.31.31.31.31. + =+ +8 8 01 1a ax x32.32.32.32.32. 25 32 71 1 1m m ma a a = 33.33.33.33.33. + =+ +x xa a1 1034.34.34.34.34. + = += 14121 24142 2 2 2a a a am m m m35.35.35.35.35.5671210 712312141 1 1 1 1a a a a am m m m m+ + + + + == =36.36.36.36.36. 41312 131132 2 2 2a a a a ==37.37.37.37.37. + = += 53420 34174mn mn mn mn38.38.38.38.38. 8 25 172 3 2 3 2 3a b a b a bx x x x x x+ + + + + + = 39.39.39.39.39. + = +=787 8818a b a b a b a bm n m n m n m n40.40.40.40.40. 0 85 0 5 0 35, , ,mxy mxy mxy =EJERCICIO 91.1.1.1.1. 9 3 5 11a a a a + =2.2.2.2.2. + =8 9 0x x x3.3.3.3.3. 12 23 5 16mn mn mn mn = 4.4.4.4.4. + =x x x19 18 05.5.5.5.5. 19 10 6 15m m m m + =6.6.6.6.6. + =11 15 26 0ab ab ab7.7.7.7.7. + = 5 9 35 31a a a aX X X X8.8.8.8.8. + =+ + +24 15 39 02 2 2a a aX X X9.9.9.9.9.23132 1 33030y y y y y+ =+ = =10.10.10.10.10. + = + = 35141212 5 10201720m m m m m11.11.11.11.11.38143 2 88382 2 2 2 2a b a b a b a b a b+ =+ = 12.12.12.12.12. + + =a a a a a8 9 1513.13.13.13.13. 7 11 20 31 15ab ab ab ab ab + = 14.14.14.14.14. 25 50 11 14 02 2 2 2x x x x + + =15.15.15.15.15. + =xy xy xy xy xy8 19 40 1216.16.16.16.16. 7 21 80 53ab ab ab ab ab+ = 17.17.17.17.17. + + =25 11 60 82 362 2 2 2 2xy xy xy xy xy18.18.18.18.18. + + =72 87 101 243 157ax ax ax ax ax19.19.19.19.19. + =82 71 53 206 0bx bx bx bx20.20.20.20.20. 105 464 58 301 03 3 3 3a a a a + + = 4. 21.21.21.21.21.1213141530 20 15 12601360x x x x x x + = + =22.22.22.22.22.1313161124 4 2 112112y y y y y y + = + =23.23.23.23.23.35161318 5 10 30307302 2 2 22 2a b a b a b a ba b a b + = + = 24.24.24.24.24. + = + = = 56163820 4 24 924924382 2 2 22 2 2ab ab ab abab ab ab25.25.25.25.25. + + = a a a a a a8 11 15 75 6426.26.26.26.26. + + + =7 21 14 30 82 80c c c c c c27.27.27.27.27. + + =mn mn mn mn mn mn14 31 2028.28.28.28.28. a y a y a y a y a y2 2 2 2 27 93 51 48 0 + + =29.29.29.29.29. + + + =a a a a a a a3 6 330.30.30.30.30.122376123 4 7 3 663612x x x x xx x x+ + =+ + = = 31.31.31.31.31. + + + = + + + = = 234145648 18 6 24 2024202456x x x x xx x x32.32.32.32.32. 7 30 41 9 73 0a a a a ax x x x x + =33.33.33.33.33. + + =+ + + + + +a a a a a ax x x x x x1 1 1 1 1 17 11 20 2634.34.34.34.34. a a a a a a a+ + + =6 20 150 80 31 8835.35.35.35.35. + = 9 11 17 81 110 9b b b b b b b36.36.36.36.36. + + + = a b a b a b a b a b a b a b2 2 2 2 2 2 215 85 131 39 16237.37.37.37.37. 84 501 604 715 231 16513402 2 2 2 2 22m x m x m x m x m x m xm x + += 38.38.38.38.38.56231458420 16 6 15 96241112437843 2 3 2 3 2 3 2 3 23 2 3 23 2 583 2a b a b a b a b a ba b a ba b a b+ +=+ +== =39.39.39.39.39. 40 81 130 41 83 91 16 28a a a a a a a a + + + = 40.40.40.40.40. + + =21 52 60 84 31 23 0ab ab ab ab ab ab abEJERCICIO 101.1.1.1.1. 7 6 9 47 6 13 9 4 1313 13a a b ba a a b b ba b+ + = = = 2.2.2.2.2. a b c b c c aa a b b c c c+ + = = + ==20 0 2 003.3.3.3.3. 5 11 9 20 15 20 25 11 12 9 1 1025 12 10x y x yx x x y y yx y + + = = = = 4.4.4.4.4. + + = = = = + 6 8 5 6 116 6 13 8 7 5 11 613 7 6m n m n mm m m m n n nm n5.5.5.5.5. + + + + + = + = + ==a b b c a c ba a a b b b c ca2 2 3 2 33 2 2 3 0 2 2 026.6.6.6.6. + + + + + + = + = = 81 19 30 6 80 2581 80 0 19 6 25 0 3030x y z y x x yx x x y y y zz7.7.7.7.7. 15 6 8 20 5 3115 8 86 5 12 20 31 118 12 112 2 22 2 2 22a ab a ab a aba a a aab ab ab aba ab + + + = = = = 8.8.8.8.8. + + + + =+ = = 3 4 6 81 114 313 6 31 214 81 114 3021 30a b a b b a a ba a a a ab b b b ba b9.9.9.9.9. + + + + + = + == 71 84 50 84 45 1871 50 45 18 4884 84 0483 4 2 3 4 2 3 33 3 3 3 34 2 4 23a b a b a b a b a b a ba b a b a b a b a ba b a ba b10.10.10.10.10. + + + + + + = + = + = = = a b c a b c a b ca a a a b b bc c ca8 2 2 19 2 3 3 3 32 3 2 2 3 02 3 0 8 19 3 142 14 5. 11.11.11.11.11. m mn m mn m m m mm m m m m m m m mn mn mnm m mn2 2 3 2 2 33 3 3 2 2 2 2 23 271 14 65 115 66 7 14 115 129 71 65 67 129 6+ + ++ = = == +12.12.12.12.12. x y x y x y x y x y x y x y x y yx y x y x y x y x y x y x y x yx y x y yx y x y y4 3 2 2 4 2 3 2 3 2 4 34 4 4 4 3 2 3 2 3 2 3 22 2 34 3 2 38 10 7 9 21 508 21 14 7 70 10 9 50 3114 7 31 + + + + + = + = = + == +13.13.13.13.13. 5 3 8 5 50 4 65 90 78 7 0 3 4 0 5 5 0 50 65 90 25251 2 3 1 2 2 3 33 3 3 2 2 2 1 1a b c a b b c cc c c b b b a ax x x x x x x xx x x x x x x x+ + + + + + + ++ + + + + + + + + + + + + + = + = = + = = 14.14.14.14.14. a x a x a xx x x x a a a ax am m m m m mm m m m m m m mm m+ + + + + ++ + + + + + + ++ + + + + + = + = + = = 2 3 2 3 2 33 3 3 3 2 2 2 23 25 8 3 5 6 55 5 3 5 8 6 3315.15.15.15.15. 0 3 0 4 0 5 0 6 0 7 0 9 3 3 30 3 0 6 3 2 7 0 4 0 7 3 3 3 0 5 0 9 3 3 42 7 3 3 3 4, , , , , ,, , , , , , , , ,, , ,a b c a b c a b ca a a a b b b b c c c ca b c+ + + + = = = = 16.16.16.16.16.12132 334163412122342 8 3474133162 18 1617634123 24147417614a b a b a ba a a a a b b b b ba b+ + + + =+ = = = === +17.17.17.17.17.352110132 23511026 1 2010131021326 1 63131310132 2 22 2 2 2 22m mn m mn mn mm m m m m mn mn mn mn mnm mn + + + =+ = + = += = 18.18.18.18.18. + + + + = += = = + = + = = = 3412562341613234739 28121912123422 3 84945616135 1 26661912942 2 132 2 22 2 2 22 2 2 2 2 22 2a ab b a ab b b aba a a a ab ab ab ab abb b b b b ba ab b 6. 19.19.19.19.19. 0 4 31380 6250 21460 4252 250380 23 16814801750 6142 4 141440 35 31 6 250175 0 35 252 2 3 2 2 32 2 2 2 2 2 2 23 3 3 3 32 3, , ,, ,, ,,,, ,,, ,x y xy y x y xy yx y x y x y xy xy xy xy xyy y y y yxy y+ + + == == = + = += = == +20.20.20.20.20.325750351250 215325350 23 15 5251325750125157 2 105015013251501 2 1 2 1 21 1 1 1 1 2 2 2 2 21 2a b a b a ba a a a a b b b b ba bm m m m m mm m m m m m m m m mm m + ++ =+ = + = +== +,,EJERCICIO 11Para resolver los problemas del 1 al 18 las literales toman los siguientes valores:a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/4a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/4a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/4a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/4a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/41.1.1.1.1. 3 3 1 2 6ab= =2.2.2.2.2. 5 5 1 2 3 5 8 3 1202 3 2 3a b c= = =3.3.3.3.3. b mn2 2212134623= = =4.4.4.4.4. 24 2412131461271461081182 32 3m n p= = = =5.5.5.5.5.23231 21223418824134 2 3 4 23a b m = = = =6.6.6.6.6.712712314121891211612189384631283 2 32c p m= = = =7.7.7.7.7. m n pb c a= = =121314141271414322 38.8.8.8.8.565611256125121 2 2 13 2a mb c = = =9.9.9.9.9. 2 2 2 3 4 9 36 62 2bc = = = =10.10.10.10.10. 4 12 41212 2 3 2 216 2 6 1223 23 3m bc = = = =11.11.11.11.11. mn a b = = = =812138 1 2166486434 3 4 312.12.12.12.12.434 13 2 341829abc= = =13.13.13.13.13. 55 212131420141125112602 222b mnp= == =14.14.14.14.14.34233422333 842 932441836613232bc=== = =15.15.15.15.15.2 2121311911332 2mn== = =16.16.16.16.16.2422412132131424621911642114442112416242 2 2 2mnn p= = === = 7. 17.17.17.17.17. 3 6423 64 2 32123 64 8 729 3 373 248 3 72 2163 63 3 633 3= = = = =b cm.18.18.18.18.18.353212535114232125 21235443225023513212535325351526752252323 33= ==== = =apbbmEJERCICIO 12Para resolver los problemas del 1 al 18 las literales toman los siguientes valores:a = 3 b = 4 c = 1/3 d = 1/2 m = 6 n = 1/41.1.1.1.1. a ab b2 2 2 22 3 2 3 4 4 9 24 16 1 + = + = + =2.2.2.2.2. c cd d2 22 221321312121913144 12 9362536+ + = + + = + + =+ +=3.3.3.3.3.acbd+ = + = + =3134129 8 174.4.4.4.4.cdmn + = + = + = += 2131261422324 22 72 636435.5.5.5.5.a b m2 2 2 2 2 23 2 6334266931623663 8 6 1 + = + = + = + =6.6.6.6.6.351223513124 212152 11 10 5545c b d + = + = + = += 7.7.7.7.7.abnacdbdm+ =+= + = + =+ = =3 41431312412612141122648 213144 6 13149349 238.8.8.8.8. b n m+ + = + + = + + =+ += =6 4146 6 21264 1 1221728 129.9.9.9.9. c a d b n d3 16 8133 31216 4148121331216142 1 8122 16 1213262 2 12 + = + = + = + = += = 10.10.10.10.10.mdab == = =612216116216 16 345634 . 8. 111111.1.1.1.1. 344313441461341461121242 12432418222 2cnm+ =+= + = + =+= =12.12.12.12.12.421621 212814124816112121 1 1 02 2 2 2d n+ = + = + = + = =13.13.13.13.13.a bcb md++=++= = =3 4134 612713101221 20 114.14.14.14.14.b anm bda++ =++ = + + = + + =54 3146 4125 311421215 4 4 15 2315.15.15.15.15.12216 1121332 41614361124 384 362181623 4 4824472412324c abn am d+ = + =+ = + = += =16.16.16.16.16. 433664 43 336 661693366433664 1 1 4ba m+ = += + = + = + =17.17.17.17.17. b d c d++=+ + =++= ==223 844 212231381242 121 2432346 343418.18.18.18.18.233 242 3 433 21243142 144339443122 123332432243924328983264 9 12861872 2 2 2 2258+ + = + + =+ =+ = + = + =+ = =a b da nEJERCICIO 13Para los problemas 1 al 24 las literales toman los siguientes valores:a = 1 b = 2 c = 3 d = 4 m = 1/2 n = 2/3 p = 1/4 x = 01.1.1.1.1. ( ) ( )a b c d+ = + = = =1 2 3 4 3 3 4 9 4 52.2.2.2.2. ( )( ) ( )( )a b b a+ = + = =1 2 2 1 3 1 33.3.3.3.3. ( )( )b m c n a + = + = + = + = + =+= =4 2123234 14 129 234327347247 8215272 2 124.4.4.4.4. ( )( ) ( )( )2 3 4 2123234142 1 2 1 4 3 5 152 2m n p b+ + = + + = + + = =5.5.5.5.5. ( )( )( ) ( ) ( )4 8 6 4128141 2 6234 2 2 3 0 02 2 2 2m p a b n d+ + = + + = + = 9. 6.6.6.6.6. ( )( )( )( ) ( )( )( )c b d c b a m p = = =3 2 4 3 2 112141 1 12 14147.7.7.7.7. ( ) ( ) ( )b c d a m n x2 2 2 2 562 2 3 4 112232 0 4 73 462876168 76161626+ + + = + + + = + = == =8.8.8.8.8. ( ) ( ) ( )2 6 4 2120 6 2 3 4 4 6 4 9 4 16 6 13 64 78 64 142 2 2 2 2 2mx b c d+ + = + + = + = = =9.9.9.9.9.8916 8129231614214183424622322 63832 23mnpba+ =+ = + = + = + =+= =10.10.10.10.10. ( ) ( ) ( )x m a d cb c a+ + = + + = + = =0121 4 3121 64 31262 312 3 111.11.11.11.11. ( )44121411 2342 141 494345935927552 222 2225m paa bc++=++=+ += = = =12.12.12.12.12. ( )( )( )( )( )( )2 3 4 8 6 4 9 2021232341481462341292320141 2 1 2 4 2 6 5 4 4 11 176m n p p n m n p+ + + += + + + + = + + + + = =13.13.13.13.13. ( ) ( ) ( )c m n d m p b n p2 2 22 2 2 21216312234121422314976163441112212124412126 144 441226122 2+ + + += + + + + = + = + = += = =14.14.14.14.14.c da dm2 2 2 2122 3 4124129 16122122512212512522+ =+ =+ = = = =15.15.15.15.15. ( )( ) ( )( )( )( ) ( )( )4 2 18 24 2 8 2 404142 2 182324142 8122 40141 1 4 12 6 2 4 2 11 5 6 2 66 30 132 162p b n p m p a+ + + += + + + + = + + + = + = + =16.16.16.16.16.adbd bmp++=++=++= += += = = =521424 25212142 42252141166225 8116325 81163213116322086242312222217.17.17.17.17. ( ) ( )a b c b m n+ + = + + = = = == = =2 2 2246238 1 2 3 8 212233 2512233 526152690 2688614 1418.18.18.18.18.( ) ( )a c nbc d p++ + =++ + = + = =26 1 3262323 414424271227247 10. 19.19.19.19.19. ( ) ( )( ) ( )3 32 2 1623 3 2 32122 4 1 16142233 16 6 4623 4 6 2 3 12 12 3 3c b m d a pn = = = = = 20.20.20.20.20.( )( )62 8326 1 2 32 8 2312232 2 13 423141 2 3362 16122668121318 12 82422241112abcbmnb acdnpabc+= + =+ = + =+ = =21.21.21.21.21. ( )( ) ( )( )a bb aa b a b2 22 22 22 2233 2 31 22 13 1 2 2 1 3 2533 3 853725 2163221373++ + + =++ + + = + = + =+= =22.22.22.22.22. ba b b c n m22222 2121 1 1 1 1 121112121312311243256322 4547221449470435217+ + + + += + + + + += + + + = + + = + = = =23.23.23.23.23.( )( )( )( )2 3 4 2 42123234142 3 412231 2 1 6 414493 7492149189 491859202 22 259m n p c m n+ + = + + = + + = = == =24.24.24.24.24.bcab mnb m2 2322332 1 212232123412233237249674954 28632663= = = = ==EJERCICIO 141.1.1.1.1. a b m+ +2.2.2.2.2. m b x2 3 4+ +3.3.3.3.3. a a+ +1 2;4.4.4.4.4. x x 1 2;5.5.5.5.5. y y y+ + +2 4 6; ;6.6.6.6.6. ( )$ a x m+ +7.7.7.7.7. m n8.8.8.8.8. ( )bs x. 69.9.9.9.9. ( )x m Km10.10.10.10.10. ( )$ x a m+ 11.11.11.11.11. ( )m a b c Km 12.12.12.12.12. ( )$ n 30013.13.13.13.13. ( )365 x das14.14.14.14.14. $ ; $15 ; $8a a ma15.15.15.15.15. 2 32a bc+ +16.16.16.16.16. a b m 217.17.17.17.17. 23 2n m18.18.18.18.18. x m2 219.19.19.19.19. ( ) ( )$ ; $3 6a b ax bm+ +20.20.20.20.20. ( )( )a b x y+ +21.21.21.21.21. ( )$ 8 48x +22.22.22.22.22. ( )( )bs a x. +8 423.23.23.23.23.75xsucres24.24.24.24.24. $am 11. 25.25.25.25.25.3 0001.ncolones26.26.26.26.26.xasoles327.27.27.27.27.mm1428.28.28.28.28.xakmh+1EJERCICIO 1529.29.29.29.29. $a bm+230.30.30.30.30. x xxhab+ +22.31.31.31.31.31. 1000324. + +aa asucres1.1.1.1.1. m n m n, +2.2.2.2.2. ( )m n m n m n, + = 3.3.3.3.3. +3 4 3 4a b a b,4.4.4.4.4. 5 6 6 5b a a b, +5.5.5.5.5. ( )7 6 7 6 7 6 1, + = =6.6.6.6.6. + =6 9 6 9 3,7.7.7.7.7. +2 3 2 3x y x y,8.8.8.8.8. ( )5 5 5mn m mn m mn m, + = 9.9.9.9.9. 5 7 5 7 12a a a a a, + =10.10.10.10.10. ( ) + = = 8 5 8 5 8 5 13x x x x x x x,11.11.11.11.11. + = 11 8 11 8 3m m m m m,12.12.12.12.12. 9 15 9 15 6ab ab ab ab ab, = 13.13.13.13.13. = xy xy xy xy xy, 9 9 1014.14.14.14.14. ( )mn mn mn mn mn mn mn, + = = 11 11 11 1015.15.15.15.15.12231223a b a b, 16.16.16.16.16.35343534b c b c, +17.17.17.17.17.1323132333b b b b b b, + = =18.18.18.18.18. = = 1212121222xy xy xy xy xy xy,19.19.19.19.19. = = 3525352555abc abcabc abc abc abc,20.20.20.20.20. + = += 43843832 382982 22 2 2 2x y x yx y x y x y x y,21.21.21.21.21.383438343 6838mn mnmn mn mn mn, == 22.22.22.22.22. a b c a b c, , + +23.23.23.23.23. a b c a b c, , +24.24.24.24.24. a b c a b c, , +2 225.25.25.25.25. 3 2 4 3 2 4m n p m n p, , +26.26.26.26.26. a ab b a ab b2 2 2 27 5 7 5, , 27.27.27.27.27. x xy y x xy y2 2 2 23 4 3 4, , 28.28.28.28.28. x x y x x y3 2 3 26 6, , +29.29.29.29.29. 2 3 2 3 5a b a a a b a b, , + = 30.30.30.30.30. + = m n n m n n m n, ,8 4 8 4 431.31.31.31.31. + = 7 8 7 8a a b a a b a b, ,32.32.32.32.32.1223341234234 68231423x y xx x y x y x y, , + =+ = +33.33.33.33.33. = = 352335233 55238523m m mnm m mn m mn m mn, ,34.34.34.34.34. + + = + +7 5 37 5 3 8 5 32 2 22 2 2 2 2a ab b aa a ab b a ab b, , , 12. 35.35.35.35.35. + = 7 17 5 4 10 92 2 2mn mn m m mn m36.36.36.36.36. x x x y x y x x y3 3 2 2 3 27 8 4 5 6 4 5 + + = +37.37.37.37.37. 5 9 6 7 4 3 72 2 2 2 2x x xy xy y x xy y + + = + +38.38.38.38.38. + = 8 5 11 79 6 72 2 2 2 32 2 3a b a b ab ab ba b ab b39.39.39.39.39. m m n m n mn nm m n mn n3 2 2 2 33 2 2 38 7 77 + + = + 40.40.40.40.40.1214231562 1410 31561413156a a b ba b a b + + =++ = + 41.41.41.41.41. a a b b c c b + + =3 4 8 842.42.42.42.42. m m m m n m n mnm m n mn3 3 3 2 2 23 2 25 5 4 4 78 7+ = 43.43.43.43.43. 9 11 6 4 6 8 17 2x x y y z z x y z + = 44.44.44.44.44. 6 9 5 7 8 1115 5 15 112 2 2 22 2a a ab b ba ab b+ = 45.45.45.45.45. + + = x y x y xy xy yxy y2 2 2 2 3 3 43 45 7 4 82 4 846.46.46.46.46. 312124 66 121 22252122a a b ba b a b + +=++ = +47.47.47.47.47.1234231356562 342 1354132 2 2 22 2x x xy xy y yx xy x xy+ + + =++= +48.48.48.48.48. 5 5 6 5 8 81 1 1 2 2ax ax a a a a ax x x x x + + + =+ + + + +49.49.49.49.49.3423131353 44331 153741632 2 2 22 2 2 2x x xy xy y yx xy y x xy y+ + +=+ ++= +50.50.50.50.50.34141212563 1 443 3 5632162 2 2 2 2 22 2 2 2a b a b a b ab ab aba b ab a b ab + + + = +++ = +EJERCICIO 161.1.1.1.1. 3 22 35 5a b ca b ca b+ + ++2.2.2.2.2. 7 4 57 4 6a b ca b cc + + 3.3.3.3.3. m n pm n p+ +04.4.4.4.4. 9 3 545 4 93x yx yx yx + + + 5.5.5.5.5. a b ca b ca b cb+ + +2 2 23 326.6.6.6.6. p q rp q rp q rr+ + ++ 2 6 35 847.7.7.7.7. + + +7 4 610 20 85 24 22x y zx y zx y zx8.8.8.8.8. + + + 2 3 63 8 85 104 4 8m nm nm nm n9.9.9.9.9. + + 5 2 37 3 58 5 36a b ca b ca b ca c10.10.10.10.10. ab bc cdab bc cdab bc cdab+ + + +8 3 35 2 2211.11.11.11.11. ax ay azax ay azax ay azay az + ++5 7 64 9 812.12.12.12.12. 5 7 84 63 8 92 23x yx yx yx + + + + +13.13.13.13.13. + + am mn sam mn sam mn sam mn6 45 63 5 2414.14.14.14.14. 2 36 489 4a bb ca ca b c+ ++ +15.15.15.15.15. 6 34 555 7m nn pm pm n + 16.16.16.16.16. 2 35 48 67 910 3 12 7a bcaca b c++ ++ + + 17.17.17.17.17. 2 35 96 43 58 5x yzxyx z+ ++ 13. 21.21.21.21.21. 5 3 78 5 911 5 1614 7a a aa a aa a aa ax m nx m nx m nx m + + + +22.22.22.22.22. 6 7 54 75 3 125 11 61 2 31 2 31 2 31 2 3m m mm m mm m mm m ma a aa a aa a aa a a+ + ++ + ++ + ++ + + + + +23.23.23.23.23. 83 4 2 34 5 3 49 23 2x y z ux y z ux y z ux y z uy z u+ + + ++ + + ++ +7.7.7.7.7. m nn mnm nm mn2 222 224 35 54 3++ 8.8.8.8.8. 34 54 63 1323 2x xxx xx+ + + 9.9.9.9.9. x xy yx xy yx xy yx xy y2 22 22 22 233 233 2 + + + + 10.10.10.10.10. a ab ba ab ba ab bb2 22 22 22352 8 ++ + 11.11.11.11.11. + + + + 7 5 64 8 97 144 6 12222x xx xx xx x18.18.18.18.18. 8 357 419 3a b ca b ca b ca b ca c+ + ++19.19.19.19.19. 7 2 49 6 53 68 3 515 7 3 10x yy zy zx yx y z+ + + + + 20.20.20.20.20. + + ++ + + m n pm nm pm nm n p2 56 3 45 2 83 2 924.24.24.24.24. a b c da b c da b c da b c da c+ + + + + + +2 3 23 3 43 225.25.25.25.25. 5 3 42 2 32 4 33 62ab bc cdbc cd deab bc deab bc cdab ++ + + + 26.26.26.26.26. a bb cc da cc da da da+ +212.12.12.12.12. a aa aa aa a a33 223 24 52 67 42 11 15 + ++ + +13.13.13.13.13. + + + + x xx xx xx x23 23267 58 58 9 614.14.14.14.14. a ba b aba ab ba a b ab b3 32 23 2 33 2 2 35 472 5 11 2+ + 15.15.15.15.15. x xy yx x y yx xy yx x y xy y3 2 33 2 33 2 33 2 2 352 4 54 5 3 5+ + 16.16.16.16.16. ++ + + ++ +7 467 56 82 33 2 33 2 32 3m n nm mn nm m n nmn n1.1.1.1.1. x xx xx x222452+2.2.2.2.2. a abab ba ab b222 22+ + +3.3.3.3.3. x xxx x x323 2242 4+ + + +4.4.4.4.4. a aa aa a a a4 234 3 2343 4+ ++ +5.5.5.5.5. ++ + +x xxx x x233 2363 66.6.6.6.6. x xxxx x22247 63 54 11 1 + +EJERCICIO 17 14. 17.17.17.17.17. x x xx xx xx x x x4 23 224 3 24 57 4 62 3 11 ++ ++ ++ + +18.18.18.18.18. + + ++ ++ + + + a aa aa aa a a a a6 45 33 26 5 4 3 263 814219.19.19.19.19. x xx xx xx x x x x54 235 4 3 293 7 63 4 53 3 7 3 2+ + + ++ +20.20.20.20.20. a aaa aaa a3222354 78 65 1++ ++ + + 21.21.21.21.21. x x yx y xyxy yx yx x y x y xy y4 2 23 33 42 24 3 2 2 3 45 644 65 5 2 6 + + + + 22.22.22.22.22. + + + + + + + x xyx xy yx xy yx xy yx xy y22 22 22 22 24 76 56 47 723.23.23.23.23. a ax xax x a xa x a xa ax xa x3 2 32 3 23 3 23 2 33 386 53 5145 2 + + + 24.24.24.24.24. + + + + + + 8 654 4 37 4 63 3 6 62 2 33 2 33 2 22 23 2 2a m am ma am ma a m ama m ama a m am25.25.25.25.25. x x y xyx y x y yx y xy yx xy yx x y x y x y5 3 2 44 2 3 53 2 4 55 4 55 4 3 2 2 32 33 45 22 2 2 3 + + + + ++ + +26.26.26.26.26. a a aa aa aa a aa a a5 6 24 325 26 4 363 8 54 6 54+ ++ + ++ + + + + + +27.27.27.27.27. a ba b a b aba a b a ba b a b ba ab b4 43 2 2 34 3 2 23 2 2 44 3 43 5 44 3 32 4 + + + 28.28.28.28.28. m n m nn m n mnm n mnm n m nmn3 3 23 2 23 3 23 3 2264 562 211 ++ + + + 29.29.29.29.29. a aa aa aa aa a a ax xx xx xx xx x x x+ ++ ++ + + 35 67136 321 33 41 31 2 430.30.30.30.30. + + + + + + + + + + ++ + + ++ + ++ + +a a aa a aa a aa a aa a a aa a a ax x xx x xx x xx x xx x x xx x x x1 23 1 23 21 2 21 3 23 2 134 52 33 2 15. EJERCICIO 181.1.1.1.1.12131214122 3614125614222 2 2 2x xyxy yx xy y x xy y++ ++++ = + +2.2.2.2.2. a abab bab ba ab b a b2222 2 2 212141214152 1 145 210310+ + + += +3.3.3.3.3. x xyxy yxy yx xy yx xy y x xy y2222 22 2 2 2231656234 1 563 2326531353+ + ++ ++= + = +4.4.4.4.4.3412251611013344 1103 1 26343102 2222 2 2x yxy yxy yx xy y x xy ++ ++ ++ + += 5.5.5.5.5.2315125611016112120138 10 1124 2 1203 1 261712320461712320232 22 22 22 22 2 2 2a ab ba ab ba ab ba ab ba ab b a ab b+ + + + + ++ + = + = + 6.6.6.6.6.5623341618121314565 1 2616 3 6249 6 10122672413121313127242 22 22 22 22 2 2 2x y xyx y xyx y xyx y xyx y xy x xy y + + + + + + ++ += + + 7.7.7.7.7. a ab bab b a ba b a ba ab b a ba ab b a b a a b ab b3 2 32 3 23 3 23 2 3 23 2 3 2 3 2 2 312382561435124 144 385 10 355 365478852654137885 + + ++ + += + + 8.8.8.8.8. x xx xx x xx x x xx x x x x x x x4 234 34 2 34 2 3 4 3 25323383556345 3524 563 6825296982532982 + + + + +++ = + + + +9.9.9.9.9.231425183516122 332 182 3 551 3653186526531318653 2 32 3 23 3 23 2 3 23 2 3 2 3 2 2 3m mn nmn n m nm n m nm mn n m nm mn n m n m m n mn n ++ + ++ ++ += 10.10.10.10.10. x x y yx x y y xyx y y x yx x y y xy x yx x y y xy x yx x y x y xy y4 2 2 44 2 2 4 32 2 4 34 2 2 4 3 34 2 2 4 3 34 3 2 2 3 42275638114161417566 5616 3 284 1 2141656161785141656165617816514+ + + + ++ + + = + + + + 16. 11.11.11.11.11. x x xx x xx x xx xx x x x xx x x x xx x x x x5 35 23 2 435 3 2 45 3 2 45 4 3 2234531103816142311235428 2 1128 1 6103 2823427121310182342237121813104 + ++ + + + + ++ = + + + + 12.12.12.12.12.2956133778192312142 696 71420 21 6243 1949114724493 2 32 2 33 2 23 2 2 33 2 2 3a ax xa x ax xa a x axa a x ax xa a x ax x+ + + ++ + = + 13.13.13.13.13. a a aa a aa aaa a a a a aa a a a a aa a a a a a6 4 25 34 26 4 2 5 36 4 2 5 36 5 4 3 2353812375863867 378 5835384 381073835387835107383878 ++ + + ++ + = + + + + 14.14.14.14.14. x yx y xy yy x y x yx y y x yx x y xy y x y x yx x y xy y x y x yx x y x y x y xy y5 53 2 4 55 4 2 33 2 5 45 3 2 4 5 4 2 35 3 2 4 5 4 2 35 4 3 2 2 3 4 51103416193556251321 4103418 3 2 6183 105563103429181355613531056342918+ + ++ + ++= + + EJERCICIO 19Para los problemas 1 al 14 las literales toman los siguientes valores:a = 2 b = 3 c = 10 x = 5 y = 4 m = 2/3 n = 1/51.1.1.1.1. 4 53 6 82 82 4 8 8 8 0x yx yx yy + + = =2.2.2.2.2. x xx xx xx x222225 810 306 5 506 10 726 5 10 5 72 6 25 50 72150 50 72 172 + + + + + = + = + = 3.3.3.3.3. x yx x yx x y xyx y x y x y xyx x y x y xy y4 44 2 24 3 34 4 2 2 3 34 3 2 2 3 44 3 2 2 3 42 5 84 7 105 8 7 107 5 10 85 7 5 4 5 5 4 10 5 4 4 8625 28 125 5 25 16 50 64 256 8625 3 500 2 000 3 200 256 8 3 811 + + + + + + = + + = + + = + + =. . . .4.4.4.4.4. 3 5 66 20 812 20 129 45 2923451521834552 6 9 2 1m nm nm nm n + + + + = + = + = 17. 5.5.5.5.5. nx cn abnx cn abnx abnx cn ab+ = = = 8 2510 3 510155 10153 2 3 55051056 3 510 2 18 5 156.6.6.6.6. a ba b ab ba aba b ba ab b3 32 2 33 22 33 2 33 2 33 85 6 83 24 2 2 84 2 2 2 3 2 3 84 8 4 9 2 27 832 36 54 8 42+ + ++ + + + += + += + + = 7.7.7.7.7. 27 1259 2514 810 1127 22 125 82723231522231512515827827491544312512511258844544751 84454475120 1323 32 222 23 2 2 33 2 2 3m nm n mnmnm n mnm m n mn n+ + + ++ + + + + + = + + + = + + + = + +=+ + 2252253772251152225= =8.8.8.8.8. x y mx y my mx y ma b xa b xb xa b x + + + + + = + =1 2 41 2 42 41 2 42 1 3 25 42 2 23 23 2 33 5 2 4 32315 8 2 219.9.9.9.9. n mn mn mmb xb xb xx + ++ = =1 31 31 335 3 285 3 104 5 1823234910.10.10.10.10. x y xyx y x x yxy x yxy yx y xy x yx x y xy y3 33 4 2 23 2 23 43 3 4 44 3 3 44 3 3 455 66 23 16 4 26 4 25 6 5 4 4 5 4 4 2625 24 125 20 64 256 2625 3 000 1280 256 2 2 091 + + + ++ + + + + += + += + += + + =. . .11.11.11.11.11.342313191613342 166 1 39341649342162 3493344166499 3 1 4 62 2222 22 22 2a bab bab ba ab ba ab b+ ++ +++ = + + = + = + =12.12.12.12.12.91725341473451712157341430318 7 73425 10341 2 1 1244518343534124459174535343917234523153534153917499015353412532 22 222 22 22 22 2m nm n mnm mnm n mnm n mnm mn n+ + + ++ +++ + += + + + += + += + += + + = + =+ = = 41763585034177170340 7 5101704631702 123170 18. 14.14.14.14.14. 0 2 0 4 0 50 6 0 3 0 80 4 0 8 60 2 15 0 901 01 601 01 601 2 3 2 3 01 3 60 3 4 2 9 01 27 612 18 2 7 625 53 2 22 2 33 23 2 32 2 32 2 32 2 3, , ,, , ,, ,, , ,, ,, ,, ,, ,, ,,a ab a bab a b ba a ba a b bab a b ba b ab b+ + ++ + + + + + += + + += + + += + + +=13.13.13.13.13. 12352341106141254182354 6 2 1830 5 2 1005010 30 20 3578675043578323675010154357 9 2246750435126246702504352146725435525 268 8601001 65310016222222 253100b m cnb m cnb m cnb m cnb m cnb m cn + + + + ++ + + ++ + + + + + = + += + + = + + = + +=+ += =.EJERCICIO 201.1.1.1.1. = 8 5 132.2.2.2.2. = 7 4 113.3.3.3.3. 8 11 3 = 4.4.4.4.4. ( ) = + =8 11 8 11 35.5.5.5.5. ( ) = + =1 9 1 9 86.6.6.6.6. 2 3 2 3a b a b = 7.7.7.7.7. 3 2 3 2b b = 8.8.8.8.8. 4 6 4 6x b x b = 9.9.9.9.9. = 5 6 5 6a b a b10.10.10.10.10. ( ) = +8 3 8 3x x11.11.11.11.11. = 9 5 9 52 2 2 2a b a b12.12.12.12.12. ( ) = +7 5 7 5xy yz xy yz13.13.13.13.13. 3 4a a a = 14.14.14.14.14. 11 25 142 2 2m m m = 15.15.15.15.15. ( ) = + = 6 6 52 2 2 2 2x y x y x y x y x y16.16.16.16.16. ( )11 7 11 7 183 2 3 2 3 2 3 2 3 2a m a m a m a m a m = + =17.17.17.17.17. ( ) = + =8 8 8 8 02 2 2 2ab ab ab ab18.18.18.18.18. ( )31 46 31 46 772 2 2 2 2x y x y x y x y x y = + =19.19.19.19.19. ( ) = + =84 84 84 84 02 2 2 2a b a b a b a b20.20.20.20.20. 3 5 3 51 2 1 2a b a bx x x x+ + + + = 21.21.21.21.21. = + +8 11 8 112 2x xa a22.22.22.22.22. ( )6 5 6 5 11a a a a an n n n n = + =23.23.23.23.23. ( ) = + = 45 60 45 60 151 1 1 1 1a a a a ax x x x x24.24.24.24.24. ( )54 86 54 86 1401 1 1 1 1b b b b bn n n n n = + =25.25.25.25.25. ( ) = + =35 60 35 60 25m m m m ma a a a a26.26.26.26.26. 51251210 121125 12 = + =+= =27.27.27.27.27. = = 23348 912171228.28.28.28.28.13231323332 2 2 2 2 2x x x x x x = + = =29.29.29.29.29.455624 253049303 3 3 3x y x y x y x y =+=30.30.30.30.30. = +=18341 68582 2 2 2ab ab ab ab31.31.31.31.31. = 2 3 532.32.32.32.32. ( )7 1 7 1 8 = + =33.33.33.33.33. ( ) = + = 8 5 8 5 334.34.34.34.34. ( )5 4 5 4 9 = + =35.35.35.35.35. ( ) = + =7 7 7 7 036.36.36.36.36. ( )2 5 2 5a a = + 19. 37.37.37.37.37. = 3 3x b x b38.38.38.38.38. = 2 5 2 5n m n m39.39.39.39.39. ( )3 6 6 3b a a b = +40.40.40.40.40. ( )8 5 5 83 3b a a b = +41.41.41.41.41. ( ) = +7 9 7 9a a42.42.42.42.42. ( )25 25 25 25ab ab = +43.43.43.43.43. ( )3 3 4a a a a a = + =44.44.44.44.44. ( ) = + = 4 3 4 3b b b b b45.45.45.45.45. ( )54 11 54 11 653 3 3 3 3x x x x x = + =46.46.46.46.46. 78 14 642 2 2a b a b a b =47.47.47.47.47. ( ) = + = 54 43 54 43 112 2 2 2 2a y a y a y a y a y48.48.48.48.48. = ab ab ab9 1049.49.49.49.49. ( ) = + =31 31 31 31 02 2 2 2x y x y x y x y50.50.50.50.50. = 3 4a a ax x x51.51.51.51.51. ( )311 7 311 7 3181 1 1 1 1a a a a ax x x x x+ + + + + = + =52.52.52.52.52. 105 9 96m m mx x x =53.53.53.53.53. = 31 18 491 1 1a a ax x x54.54.54.54.54. ( ) = + = 236 19 236 19 217m m m m ma a a a a55.55.55.55.55. = + + +85 54 1392 2 2a a ax x x56.56.56.56.56. ( )146146 = +a a57.57.57.57.57. ( ) = +=2352 15313358.58.58.58.58. = = = 7103856 3080868043403 33 3 3m mm m m59.59.59.59.59.56111210 11122112742 2 2 22 2 2 2 2 2a b a ba b a b a b =+= =60.60.60.60.60. = == 19451 40594069453 2 3 23 2 3 2 193 2a b a ba b a b a bEJERCICIO 211.1.1.1.1. a ba bb+ +22.2.2.2.2. 2 323 5x yx yx y3.3.3.3.3. 83 411 4a baa b++ 4.4.4.4.4. x xxx x2235 62 6+ 5.5.5.5.5. a a ba b aba a b ab3 22 23 2 27 98 9 6.6.6.6.6. x y zx y z + + 07.7.7.7.7. x y zx y zx y z+ + + 2 2 28.8.8.8.8. x y xyx y xyx y xyx xy y2 22 22 22 233 42 22 2+ + + + + + +9.9.9.9.9. x xx xx x x3 223 265 6 46 4 + + +10.10.10.10.10. y yy y yy y y yy y y y2 32 42 4 34 3 26 83 2 64 2 6 6 82 6 4 6 8+ + + + 11.11.11.11.11. a ab aa a ba ab a a ba a b ab a3 223 2 23 2 26 98 15 56 17 15 515 6 17 5 ++ + + 12.12.12.12.12. x xy yy x y x yx xy y x y x yx x y x y xy y4 3 44 3 2 24 3 4 3 2 24 3 2 2 3 49 1120 8 69 31 8 68 6 9 31+ + ++ + + + + + 13.13.13.13.13. a b c da b c da b+ + + ++2 214.14.14.14.14. ab ac cd deab ac cd deab ac cd de+ + + + + 2 3 58 4 5 57 6 2 1015.15.15.15.15. x x xx x xx x x3 23 23 26 9 196 11 21 435 17 30 24+ + + + + 20. 16.16.16.16.16. y y yy y y yy y y y y y y y y y5 3 23 2 45 3 2 4 5 4 3 29 6 3131 8 11 1940 14 11 19 31 11 40 14 19 31 + + + + + + + + + + 17.17.17.17.17. 5 9 6 85 21 14 189 27 22 18 27 22 9 183 3 2 23 2 23 2 2 2 2 3m n m n mnm m n mnn m n mn m n mn n + + + + + +18.18.18.18.18. 4 19 625 51 3229 32 38 29 38 323 3 4 2 23 3 2 2 43 3 4 2 2 4 4 3 2 2 3 4x y xy y x yx y xy x y xx y xy y x y x x x y x y xy y + + ++ + + + + +19.19.19.19.19. m m n m nm n m n mnm m n m n m n mn m m n m n m n mn6 4 2 2 42 4 3 3 56 4 2 2 4 3 3 5 6 4 2 3 3 2 4 59 1930 61 13 1621 80 13 16 13 21 16 80+ ++ + + + + + + + + + +20.20.20.20.20. + ++ + + + + +a b a b aba a b a b ba a b a b a b a b ab b5 3 3 56 4 2 2 4 66 5 4 2 3 3 2 4 5 66 18 428 11 11 98 11 6 11 18 9 4221.21.21.21.21. 1 3 624 30 8 1525 29 7 12 6 6 7 29 12 252 4 3 52 4 62 4 3 5 6 6 5 4 3 2 + + + ++ + + +x x x x xx x x xx x x x x x x x x x x x22.22.22.22.22. + + + + + + + + + + + + 6 8 23 80 1851 21 80 96 8 28 101 98 9 8 28 101 6 9 982 3 5 4 3 24 3 2 5 42 3 5 4 3 2 5 4 5 4 3 2 2 3 4 5x y x x y x yx y x y y xyx y x x y x y y xy x x y x y x y xy y23.23.23.23.23. m m n m n mnm n m n mn nm m n m n m n m n mn n6 4 2 2 4 55 3 3 5 66 5 4 2 3 3 2 4 5 68 21 6 823 14 24 8 1423 8 14 21 18 8 22 + + + ++ + + +24.24.24.24.24. x x x xx x x xx x x x x x x x x x x x x x7 5 26 4 37 5 2 6 4 3 7 6 5 4 3 28 16 23 1551 18 8 25 3059 16 23 3 8 25 30 8 16 25 30 23 59 3 + + + + + + + + + + + +25.25.25.25.25. 9 15 31 1415 3 25 53 99 31 4 25 53 9 14 9 25 53 31 9 4 146 4 2 2 4 64 2 6 5 3 3 56 2 4 6 5 3 3 5 6 5 3 3 2 4 5 6a a b a b ba b b a b a b aba a b b a b a b ab a a b a b a b ab b + ++ ++ + + + + +26.26.26.26.26.a a aa a aa ax x xx x xx x+ + + ++ ++ ++1 21 215 64 7 21. 27.27.27.27.27. m m mm m m mm m m m m m m m m ma a aa a a aa a a a a a a a a a + + + + + 1 22 1 31 2 1 3 1 1 2 334 5 3 85 2 3 8 3 5 2 828.28.28.28.28. a a a aa a a aa a a a a a a a a a a am m m mm m m mm m m m m m m m m m m m+ + + + ++ + + + + + + + ++ + + ++ + + + + + + +4 2 12 1 3 14 2 1 3 1 4 3 2 1 17 8 614 8 5 117 8 14 5 11 5 7 11 8 1429.29.29.29.29. x x x xx x x xx x x x x x x x x x x xa a a aa a a aa a a a a a a a a a a a+ + + + + + + + + + + + + 2 1 21 1 32 1 2 1 3 2 1 1 2 37 9 2519 45 11 6026 36 25 11 60 11 26 36 25 6030.30.30.30.30. m m m mm m m m mm m m m m m m m m m m mn n n nn n n n nn n n n n n n n n n n n+ + + + + + 1 2 3 52 3 5 41 2 3 5 4 1 2 3 4 56 8 195 6 9 811 2 28 8 8 11 2 28EJERCICIO 221.1.1.1.1.b ab ab a a b +2 2 2 22.2.2.2.2. 2 34x yx yx y+ ++3.3.3.3.3. + + +7 552 5 2 5aa ba b a b4.4.4.4.4. + + + + + +xx xx x x x222 2652 6 5 2 5 65.5.5.5.5. x y xyxy xx y xy x x x y xy2 22 32 2 3 3 2 256 6++ + + +6.6.6.6.6. 7 56 85 8 8 52 22 32 2 3 3 2 2a b aba b aa b ab a a a b ab+ ++ + + +7.7.7.7.7. + + + a b ca b ca b c2 322 3 58.8.8.8.8. + ++ + + +3 4 52 3 4 3 2 4n m pn m pn m p m n p9.9.9.9.9. x y zx y zx y z+ ++ 3 62 2 510.10.10.10.10. + + + + +5 86 37 2 2 72 22 22 2 2 2b ab ab ab ab ab a a ab b11.11.11.11.11. + + + +5 636 92 22 22m n mnm n mnm mn12.12.12.12.12. + + + + + + 8 5 468 6 10 8 6 10232 3 3 2x xx xx x x x x x 22. 13.13.13.13.13. 14 8 1614 98 7 8 722 33 3m nm mn m m n + + +14.14.14.14.14. 8 5 667 6ab bc cdab bc cdab bc+ + + +15.15.15.15.15. a a b ba b b aba a b ab3 2 32 3 23 2 2925 834 8 + + +16.16.16.16.16. 6 8 66 46 8 7 6 43 2 22 33 2 2 3x x y xyxy yx x y xy y + + 17.17.17.17.17. m n cm n c dn c d c d n229 11 147 816 19 14 19 16 14 + + + + + +18.18.18.18.18. 5 9 40 67 8 55 2 8 45 54 3 3 43 2 2 3 44 3 2 2 3 4a a b ab ba b a b ab ba a b a b ab b+ + + + + +19.19.19.19.19. x x xx x xx x x x xx x x x x5 4 22 35 4 2 35 4 3 28 25 156 7 6 98 19 22 6 98 6 19 9 22 + + + + + + + + + +20.20.20.20.20. + + + + + +3 8 19 186 259 8 44 188 9 44 184 3 2 54 5 5 2 34 3 2 5 5 2 35 3 2 2 3 4 5xy x y yxy y x x yxy x y y x x yx x y x y xy y21.21.21.21.21. x x x xx x x xx x x x xx x x x x3 4 23 2 53 4 2 55 4 3 26 8 9 1525 18 46 25 1124 6 26 37 10 1111 6 24 26 10 37 + + + + + + + + + +22.22.22.22.22. a a b ab ba b a b a b aba a b a b a b ab b5 3 2 4 54 3 2 2 3 45 4 3 2 2 3 4 526 8 68 15 45 88 27 15 53 14 + + + + + + + +23.23.23.23.23. y y yy y y yy y y y y yy y y y y y6 3 23 4 56 3 2 4 56 5 4 3 2923 5 8 15 822 14 8 15 815 8 22 8 14+ + + + + + + + + + + + + +24.24.24.24.24. x x x xx x x xx x x x x x x xx x x x x x x x8 6 4 27 5 38 6 4 2 7 5 38 7 6 5 4 3 23 5 936 7 5 23 513 5 45 7 5 23 517 5 3 23 5 51 45 + + + + + + 25.25.25.25.25. x x y x y x yx y x y y x y xyx x y x y x y y x y xyx x y x y x y x y xy y7 5 2 4 3 2 54 3 2 5 7 3 4 67 5 2 4 3 2 5 7 3 4 67 5 2 4 3 3 4 2 5 6 73 35 8 6060 90 503 95 7 60 90 503 95 90 7 50 60 + ++ + + + + + + + +26.26.26.26.26. a aa a aa a a aa a a ax xx x xx x x xx x x x+ ++ ++ + ++ + + + + + + 3 11 23 1 23 2 18 55 63 5 63 6 527.27.27.27.27. + + + + + + + 8 16 157 5 815 16 10 815 8 10 164 2 32 3 14 2 11 2 4a a a aa a a aa a a aa a a an n n nn n n nn n n nn n n n28.28.28.28.28. 15 5 6 419 18 3115 14 6 59 3115 14 31 6 593 2 12 1 1 43 2 1 1 44 3 2 1 1x x x xx x x xx x x x x xx x x x x xa a a aa a a aa a a a a aa a a a a a+ + + + ++ + + ++ + + + + ++ + ++ + + + + +29.29.29.29.29. 9 21 26 145 12 814 33 26 14 814 33 26 8 141 2 3 51 2 41 2 3 5 41 2 3 4 5a a aa a a aa a a a aa a a a am m m mm m m mm m m m m mm m m m m m + + + + + + + + + + + +30.30.30.30.30. + ++ + + + + ++ + + + + + + + + 15 50 14 6 823 615 23 56 14 5 83 1 1 24 2 1 14 3 2 1 1 2m m m m mm m m mm m m m m m mx x x x xx x x xx x x x x x x 23. EJERCICIO 231.1.1.1.1. 112 + +aa2.2.2.2.2. 088 + +aa3.3.3.3.3. + 93 53 4 3 422 2a aa a a a4.4.4.4.4. + + + 165 165 522 2xy xxy x x xy5.5.5.5.5. 11 13 2 23 2 2 3 2 2 + + + +a a b aba a b ab a a b ab6.6.6.6.6. xx x y xyx x y xy33 2 23 2 28 62 8 6+ ++ +7.7.7.7.7. aa b ab ba a b ab b32 2 33 2 2 38 68 6+ ++ +8.8.8.8.8. + + + +yx y x y xyx y x y xy y43 2 2 33 2 2 3 45 7 85 7 89.9.9.9.9. mm am a m a m am am a m a m a44 3 2 2 3 44 3 2 2 3 45 18 74 18 7 + + + +10.10.10.10.10. 161430 30 + + +b a c db a c d a b c d11.11.11.11.11. xxy yx xy y x xy y222 2 2 211 1 12.12.12.12.12. aa b ab ba a b ab b32 2 33 2 2 365 85 8 6+ + + +13.13.13.13.13. x yx y xyx x y xy y3 32 23 2 2 35 17 55 17 5++ ++ + +14.14.14.14.14. xx y x y xyx x y x y xy43 2 2 34 3 2 2 319 8 159 8 15 1 + + + + 15.15.15.15.15. a ba b a b a b aba a b a b a b ab ba a b a b a b ab b5 54 2 3 3 2 45 4 2 3 3 2 4 55 4 3 2 2 3 4 511 2 8 411 2 8 411 8 2 4++ ++ + + + + +16.16.16.16.16. x xx xx x x x4 234 3 2505 255 25 50+ + + + + +17.17.17.17.17. y yy y y yy y y y y yy y y y y y65 4 3 26 5 4 3 26 5 4 3 2419 17 1841 9 17 189 17 18 41+ + + + + + 18.18.18.18.18. a a b a ba b a b ab ba a b a b a b a b ab b6 4 2 2 45 3 3 5 66 5 4 2 3 3 2 4 5 6915 17 1415 9 17 14+ ++ + ++ + + + +19.19.19.19.19. x x xx xx x x x x x x x4 324 3 2 4 3 2115 3416 34 16 34+ + ++ + + + + +20.20.20.20.20. mm n mn nm m n mn n32 2 33 2 2 317 37 3 1 + + 24. EJERCICIO 241.1.1.1.1.121413252 14132534132522 22 22 2aa ab ba ab ba ab b+ ++ = + 2.2.2.2.2. 154523594523135 5945231409452315 59 + ++= += +xy yzxy yzxy yzxy yz3.3.3.3.3.3516342918 530342934133029bcbc ab cdbc ab cdab bc cd + ++ + + +4.4.4.4.4.12234529125 8106 29123108912a ba ba ba b +++= +5.5.5.5.5.5938110573115930 8805731159388057311595719403112 222 22 22 2x yy xyx y xyx y xyx xy y ++ += + +6.6.6.6.6.56291512385610 945123856123819453 33 2 23 3 2 23 2 2 3m nn m n mnm n m n mnm m n mn n++ + +++ + +7.7.7.7.7.37133551412186 5142 361141635182 2222 2a ab ba aba aba ab b+ ++ +8.8.8.8.8.385611035310215 244050 18601 20103940686021103940171521102 22 22 22 2 2 2x xy yx xy yx xy yx xy y x xy y+ + ++++= + = + 9.9.9.9.9. a a aa aa a aa a a3 223 23 25678910788 7810 91020 21241581910124+ ++ ++++= + 10 .10 .10 .10 .10 . m mn nmn n m nm mn n m nm m n mn n3 2 32 3 23 2 3 23 2 2 371247595211821 20364 775211852113611718+ + ++++ + + + + 25. 12.12.12.12.12.123578897201819781212 7207 188 197812192088997812192078a b c db c da b c da b c da b c d+ ++ + +++++= + + = + + 6.6.6.6.6. 58141378656582 781 183565898193565658981932 22 32 2 32 2 33 2 2a b abab aa b ab aa b ab aa a b ab+ + +++= + + + 7.7.7.7.7.211514136782921120 49563 29621129565963 2 2 34 2 2 34 3 2 2 34 3 2 2 3m n m n mnm m n mnm m n m n mnm m n m n mn+ + ++ +++= + + 8.8.8.8.8. + + + + ++ +++= + + = + + 78114231371237182912781 614238 32463 291278514231124659127851423112474 3 2 2 3 45 3 2 45 4 3 2 2 3 45 4 3 2 2 3 45 4 3 2 2 3 4 29x y x y x y xyx x y xyx x y x y x y xyx x y x y x y xyx x y x y x y xy1.1.1.1.1. 3856569 202456112456222 2a aaa a a a = 2.2.2.2.2. 8 6 5123516 1230 3551523355a ba ba b a b+ +++ = + 3.3.3.3.3. x x yx yx x y x x y3 223 2 3 2236796 796196+ + = 4.4.4.4.4. a b ca b ca b c a b c+ + +++= + 1234232 124 343 231274535.5.5.5.5.2356122 335 661 22131632m n pm n pm n p m n p+ + ++++= +11.11.11.11.11.353457235813563 55345815 7214 56253458821164 3 3 44 2 2 3 44 3 2 2 3 44 3 2 2 3 4x x y xy yx x y xy yx x y x y xy yx x y x y xy y+ + + + += + EJERCICIO 25 26. 9.9.9.9.9.79231821379111796 791811 1112 13137913918121115135 4 2 3 3 2 4 5 66 4 2 2 4 5 66 5 4 2 3 3 2 4 6 6 5 4 2 3 3 2 4 6x y x y x y x y xy yx x y x y xy yx x y x y x y x y y x x y x y x y x y y+ + + + + + ++ +++= + + +10.10.10.10.10.1379587112523163461 2314 3185 687112 3051118187113253 2 2 33 2 23 2 2 3 3 2 2 3x x y xy yx x y xyx x y xy y x x y xy y + + ++ += 11.11.11.11.11.310375921372051413352136 7206 5145 39352131320111429354 2 2 4 66 4 2 2 4 66 4 2 2 4 6 6 4 2 2 4 6m n m n nm m n m n nm m n m n n m m n m n n ++ ++++++ = + + +12.12.12.12.12.387227121213355115634313387 10227 1012123413 93935381722171212342239355 4 3 2 2 3 54 3 2 4 55 4 3 2 2 3 4 55 4 3 2 2 3 4 5c c d c d c d dc d c d cd dc c d c d c d cd dc c d c d c d cd d+ + + + + +++++ += + + + EJERCICIO 26Para los problemas 1 al 14 las literales toman los siguientes valores:a = 1 b = 2 c = 3 x = 4 y = 5 m = 3/2 n = 2/51.1.1.1.1. a abab ba ab b222 22 2341 4 1 2 2 1 8 4 11 = = = 2.2.2.2.2. a bb a b aba b a b ab a a b ab b3 33 2 23 3 2 2 3 2 2 33 2 2 32 5 63 5 6 5 6 31 5 1 2 6 1 2 3 2 1 5 2 6 4 3 81 10 24 24 11++ + + + + += + + = + + = + + = 27. 3.3.3.3.3.1212531 221253121253121122533121 51 2 102723 12aa b ca b c a b c + + = + + = += += =4.4.4.4.4. 3 510 82 15 8 2 8 1523283225152529448103459224512545 48 241027102 22 22 2 2 22 2m nm n mnm n mn m mn n = = = = = = 5.5.5.5.5. x x y yx y xy yx x y x y xy y4 2 2 43 3 44 3 2 2 3 44 3 2 2 3 418 1516 6 916 18 6 64 16 4 5 18 4 5 6 4 5 6 5256 80 64 18 16 25 24 125 6 625256 5120 7 200 3 000 3 750 4 926 ++ + + += + + + = + + + = + + + =. . . . .6.6.6.6.6. a am mam m a ma am m a m a a m am m3 2 32 3 23 2 3 2 3 2 2 33 22 375 5 82 6 8 8 2 61 8 1322 132632124229462781 12928144 48 18 814194 ++ + + += + = + = + = +=7.7.7.7.7.237815161104 167 882 1101218110121181 21102122841012142510 5 8203202 22 22 2 2 22 2a ab ba ab ba ab b a ab b+ ++= = = = = 8.8.8.8.8.2334121614124 163 145632563225322527856182032425278341250675 150 482008732002 2 32 2 3 32 2 3 3 2 23 2 2m n mn nm n mn n mm n mn m m m n mn+ + + +++++ = + += + + = + + = + + =+ +=9.9.9.9.9. a a b ba b a ba a b a b a b b5 2 4 54 2 3 35 4 2 3 3 2 4 55 4 2 3 3 2 4 5355 31 1 2 5 1 2 3 1 2 21 4 5 8 3 16 32 1 4 40 48 32 21 + + + += + += + + = + + =10.10.10.10.10. + + = + = + = ab mn mxabab mn mx10 81516 10 816 1 2 103225832432 6 48 7411.11.11.11.11. aa b ab ba a b ab b32 2 33 2 2 33 2 2 311 911 91 11 1 2 9 1 2 21 22 36 8 7 + + = + = + =12.12.12.12.12.16423563816423563816442345643843232063896 256 80 924231247789424 24 258xx xx x x + += += + = += = = 28. 13.13.13.13.13. x x y xyx xy yx x y xy yx x y xy y3 2 23 2 33 2 2 33 2 2 33 2 2 33162534351254 343162 3512514316151251443164 5154 51255146415161645251252516 15 20 5 56+ + ++ + + + += + + + = + + += + + + =EJERCICIO 271.1.1.1.1. + + ++ +ab b aa b a ab ba ab b ab b2 22 2 2 22 2 25 44 42.2.2.2.2. aa+ + 8 16 1414 133.3.3.3.3. ++ + + + + x xyx y yx x y xy yx yx x y xy yx x y xy y3 22 33 2 2 323 2 2 33 2 2 3455 475 412 44.4.4.4.4. + + + 3 4 53 4 5 44 5 43 2 3 43 2 3 33 4 3m n mn n mm n mn n nn m n5.5.5.5.5. 8 9 3 67 9 35a b c aa b c aa a+ + 6.6.6.6.6. a b c a b ca b c aa a b c + + + + 2214.14.14.14.14.255692 555 546354961351496113549630 18 245302573081 3 21 3 21 31 34 4 1 4 31730a a a aa a aa a aa a ax x x xx x xx x xx x x + + + + += + = + =+ += =7.7.7.7.7. + + + + +m n p m n pm n p m n pm n p2 2 208.8.8.8.8. 9 5 39 7 25 25 66 25 24 5 32 2 22 2 2 22 2 2 2ax a x ax aax a x x aa x x ax a + + + + 9.9.9.9.9. 5 6 4 12 8 6 2 5 2 22 5 2 2 5 2 32 33 3 23 2 3 2a a aa a a a aa a a a a a+ + + + + + 10.10.10.10.10.5 9 4 111 7 6 11 2 9 6 411 2 9 6 4 12 2 9 6 53 2 44 3 4 3 24 3 2 4 3 2x x xx x x x x x xx x x x x x x x + + + + + + + + 11.11.11.11.11. 35 7 117 35 8 6 7 57 5 8 52 2 3 33 2 2 3 23 2 3 2 3a b ab a ba a b ab a aba ab a ab b + + + + + + +12.12.12.12.12. + + + + + + + + + + 11 14 25 819 6 9 411 19 8 16 47 411 19 8 16 411 26 8 20 44 23 24 3 25 34 3 25 4 3 2n n nn n nn n n nn n nn n n nn n n n n 29. 13.13.13.13.13. + + + + + + + + + + +6 5 67 5 11 67 11 11 5 6 687 11 11 5 6 66 11 3 5 7 63 34 3 2 2 44 3 2 2 3 44 2 2 44 3 2 2 3 44 3 2 2 3 4a m ama a m a m ma a m a m am ma a m ma a m a m am ma a m a m am m14.14.14.14.14. + + + + + + ++ + ++ + +4 13 96 8 26 4 8 13 8 230 406 4 8 13 8 27 4 38 13 48 34 2 3 45 3 2 4 55 4 3 2 2 3 4 55 3 2 4 55 4 3 2 2 3 4 55 4 3 2 2 3 4 5x y x y xyx x y xy yx x y x y x y xy yx x y xy yx x y x y x y xy yx x y x y x y xy y15.15.15.15.15. a b aa b a ba b+ +22216.16.16.16.16. 8 9 8 6 46 5 28 6 4 8 6 6x x yyx y x y+ + ++ + + +17.17.17.17.17. x y x xy yxy y yx xy y x xy y2 2 2 22 22 2 2 26 7 347 40 9 167 34 7 43 16 + + + + 18.18.18.18.18. 4 8 5 57 6 45 22 2 2 22 2 2 22 2 2 2a ab b a ab ba ab b a ab ba ab b a b+ + + + ++ + +19.19.19.19.19. x yx y xyx x y xy yx x y xy yx yx x y xy y3 32 23 2 2 33 2 2 33 33 2 2 314 514 514 53 194 14 5 20 + + + + 20.20.20.20.20. x x y y x x y yx y y x x y yx x y y4 2 2 4 4 2 2 42 2 4 4 2 2 44 2 2 46 2 328 31 2 322 32 0 + ++ + + +21.21.21.21.21. + ++ + + + + + + + + 67 8 66 7 8 66 7 8 63 8 196 4 15 8 255 4 23 25 4 35 4 36 4 36 5 4 3n n nn n nn n n nn n n nn n nn n n n n22.22.22.22.22. a a b aba b a b ab ba a b a b ab ba a b a b ab ba b a b ba a b a b a b ab b5 3 2 44 3 2 4 55 4 3 2 4 55 4 3 2 4 54 2 3 55 4 3 2 2 3 4 53 622 10 1122 7 522 7 55 717 7 7 5 2 ++ + + + + + + + + + 23.23.23.23.23. 4 5 2 3 5 6 47 8 4 53 5 6 4 3 5 6 13 2 3 23 43 2 4 3 2m m m m m mm m mm m m m m m m + + + + + + + 24.24.24.24.24. 7 11 2 87 11 8 42 8 2 42 2 22 22 2a ab b ba ab bb b + + + + 25.25.25.25.25. 3 4 57 8 11 5 6 2 112 7 25 6 2 11 6 7 11a b ca b a b ca b c a b ca b c a b + + + + + + + + 26.26.26.26.26. 5 14 19 89 13 15 17 10 63 52 8 17 10 13 254 25 4 3 24 35 4 3 2a a aa aa aa a a a aa aa a a a a+ ++ + + + + + + + + 30. 27.27.27.27.27. m m n nm n m n mn nm m n m n mn nm m n mn nm m n m n mn nm m n m n mn n4 2 2 43 2 2 3 44 3 2 2 3 44 2 2 3 44 3 2 2 3 44 3 2 2 3 410 1511 14 311 4 3 166 7 811 4 3 165 11 11 11 17+ + + ++ + + + + + + + 28.28.28.28.28. a a b ab ba b a b ab ba b a b aba a b a b a b ab ba a b aba a b a b a b ab ba a b a b a b ab b5 3 2 4 54 2 3 4 53 2 2 3 45 4 3 2 2 3 4 55 2 3 45 4 3 2 2 3 4 55 4 3 2 2 3 4 54 87 15 25 33 57 3 18 22 23 6 21 67 3 18 22 22 7 3 24 2 6+ + + + + + + + + + + + EJERCICIO 2829.29.29.29.29. x yx y x y x y yx x y x y x yx x y x y x y xy yx x y x y x yx y x y xy y5 54 3 2 2 3 55 4 3 2 2 35 4 3 2 2 3 4 55 4 3 2 2 34 3 2 4 53 21 183 21 1832 26 18 23 21 1829 47 2++ + + + ++ + + +30.30.30.30.30. 3 6748 7 1248 7 5 1311 21 22 1 11 22 1 1 2a aa a aa a aa a a aa a aa a a a ax xx x xx x xx x x xx x xx x x x x+ + + + + + + + + + 6.6.6.6.6. a x x a x ax xa ax a a x ax xa a x ax x a a x ax xa a x ax xa a x ax xa x ax2 3 2 2 33 2 3 2 2 33 2 2 3 3 2 2 33 2 2 33 2 2 32 23 5 11 113 4 6 83 3 9 17 33 39 17 310 14 + + + ++ + + + + + +7.7.7.7.7. x xx x x x xx x x xx x x x x x x xx x x xx x x xx x x x4 23 3 24 2 44 3 2 4 3 24 3 24 3 24 3 233 5 7 8 3 45 4 32 4 2 7 8 3 12 4 27 8 3 16 12 4 1+ + + + + + + + + + + + + + + +1.1.1.1.1. x x x xx xx x x x2 22 25 4 2 12 6 6 22 1 2 2 3+ + + + + 2.2.2.2.2. 3 5 7 4 6 23 8 3 7 7 34 6 2 7 7 3 3a b c a b a b ca b c b c a b ca b c a b c a b c + + + + + +3.3.3.3.3. x x x xx x x x x xx x x x x x x3 3 23 2 2 23 2 2 3 21 9 4 6 85 7 3 1 3 8 56 8 3 8 5 6 2 8 3+ + + + + + + + + +4.4.4.4.4. a a a aa a a aa a a a a a a a2 4 3 23 43 2 4 4 3 21 21 2+ + + + + + + 5.5.5.5.5. ab bc ac ab bc ac ab bc acbc ac ab bc ac ab acab bc ac ab ac ab bc+ + + + + + + + + 5 3 4 6 9 97 8 9 3 5 4 96 9 9 4 9 3 6 9 31. 8.8.8.8.8. m nm n m n mn m m n m n mn nm m n n m n mn m m n mnm n m n mn n m m n mn m m n m n mn n4 43 2 2 3 4 3 2 2 3 44 2 2 4 2 2 3 4 2 2 33 2 2 3 4 4 2 2 3 4 3 2 2 3 417 4 7 6 17 2 7 816 80 4 217 2 7 81 2 17 3 8 81 2 + + + + + + + + + + 9.9.9.9.9. + + + + + + + + + + + + + + +a aa a a a a a a a a a aa a a a a a a a aa a a a a a a a a a a a a35 4 2 4 3 2 5 4 3 22 3 2 4 3 25 4 3 2 4 3 2 5 3 276 8 4 11 10 275 11 26 16 8 7 15 12 7 7 1511 10 27 12 7 7 15 11 4 3 4210.10.10.10.10. 3 3 20 11 811 9 14 19 8 9 3 11 8 143 11 8 14 20 11 8 17 142 2 2 2 2 22 2 2 2 22 2 2 2 2x y x xy y x xy yxy y x xy y x xy yx xy y x xy y x + + + + + + + +11.11.11.11.11. a aa aaa a + + +1 31 40 3 82 12212.12.12.12.12. a ab ba ab b a ab b a ab ba ab b ab b a ab ba ab b a ab b ab b2 22 2 2 2 2 22 2 2 2 22 2 2 2 23 8 7 9 3 45 11 17 8 7 2 92 9 4 5 + + + + + + + + + +13.13.13.13.13. mm m m m m m mm m m m m m m mm m m m m m m m m m m43 2 5 5 4 22 4 2 4 3 24 3 2 5 4 2 5 4 318 6 5 16 16 7 197 1 16 7 3 7 13 57 13 5 16 7 19 17 13 24 + + + + + + + + + + + + 14.14.14.14.14. x yx y x y x y y x y x y xy x x y x y x y xy yx y xy xy x y x y xyx x y x y x y xy y x y x y xy x x y x y x y xy y5 54 3 2 2 3 5 4 3 2 4 5 4 3 2 2 3 4 53 2 4 4 4 3 2 45 4 3 2 2 3 4 5 4 3 2 4 5 4 3 2 2 3 4 52 5 7 3 7 11 2 2 7 6 4 87 6 8 1 7 10 12 2 7 6 4 8 7 10 1 9 7 4 4 7 + + + + + + + + + + + + + + + + +15.15.15.15.15. + + + + + + + + + + + + + + + + + + + + + +a a aa a aa a a a a a a a a a aa a a a a a a a a a a a aa a a a a a a a a a a a a a a a6 45 3 24 3 4 2 5 4 3 23 2 5 3 2 6 5 4 3 26 5 4 3 2 5 4 3 2 6 5 4 37 83 11 46 11 2 8 3 7 8 5 5 3 7 48 58 135 5 4 1 5 7 41 50 8 3 5 4 14 133 5 4 14 13 5 3 7 48 58 13 8 4 2 44 244 a16.16.16.16.16. a a x a x xa x a x ax a x a x a xa x ax x aa a x a x a x ax x a a x a x a x xa a x a x a x xa a x a x a x ax x5 3 2 3 2 54 2 3 4 4 3 2 2 33 2 4 5 55 4 3 2 2 3 4 5 5 4 3 2 2 3 55 4 3 2 2 3 55 4 3 2 2 3 4 57 9 18 4 820 21 19 9 17 119 7 80 3620 2 21 26 71 9 11 4 289 11 4 2820 2 21 26 7111 + + + ++ + + + + + + + + + + + + + +a x a x a x ax x4 3 2 2 3 4 510 26 5 99 + + 32. 1.1.1.1.1. a b aa b a ba b a ba b a b+ + ++ = + = 1234233413543 232 349 412541354512542.2.2.2.2.38612355635563538656353863 56386433863 23 2 3 23 2 33a a aa a a a aa a a a aa a + + + + + + += +3.3.3.3.3. a b a ba b a ba b a ba b a b+ + + + ++++++= + + = + +3357362523615165 259 2363 1514 16635736255264.4.4.4.4.133715114296136 114291 30513514293155613514293155 2651429315765142963 223 23 233 23 23 2 15x xx xx x xx x xxx x xx x xx x x + + ++= + + + ++ + = + + EJERCICIO 295.5.5.5.5.7127123725637256341513712372567 91237251518 13433725151734 4 3 23 2 44 3 2 4 3 24 3 2a a a aa a a aa a a a a a aa a a a + + + + + + = + 6.6.6.6.6. + + + +++ + += + + = + 122314592519253125913203126 195 82031213202 155125913203121320175x y z yy z x y zx y z x zx y z x z7.7.7.7.7. + ++= + ++ +323418562312 189 10123 2311811213121311811213121181122 2 32 2 32 2 32 2 33 32 2 33 2 2a b ab ba b ab ba b ab ba b ab ba ba b ab ba a b ab8.8.8.8.8. 1229231512193513355911019110122 39356 592 110126 1101219351911012710a b b c a b cb c b c b ca b c b c a ca b c b c a c + + ++= + = + = 33. 9.9.9.9.9.131815142314131940231835341101329401813194034110135 2440342 1101310 2940232 188 91210 8801319403411013194023181122801121403 2 2 3 22 3 2 3 23 2 3 23 2 3 2a a a a a a aa a a a a a aa a a a a a aa a a a a a a a+ + + + + + + ++ ++= + = + = + = +10.10.10.10.10.35562929192335731361232131417452293212357319143510 18122 391410 17451 2294 961239 2182 14352812191427452191361237182 2 2 2 2 22 2 2 2 22 2 2 2 22 2 2 2 2x xy y x xy y x xy yxy y x xy y x xy yx xy y x xy y yx xy y x xy y y + + + + + + +++++++++= + = = += + = 34357319143573136122 2 2 2x xy y x xy y11.11.11.11.11.27151214153438327103438110541832122734381102734382 1102 542 18322 5102715 1107102734381103 3 2 2 2 2 32 2 3 2 2 3 3 2 2 33 2 2 3 2 2 3 3 33 2 2 3a b a b ab a b ab ba b ab b a b ab b a a b ab ba a b ab b a b ab b a ba a b ab b + + + + + + + + ++ + = + = + = = 34383271027141071027757102 2 3 3 3 3 3a b ab b a b a b12.12.12.12.12.131427352553514251147201423514141160144 11412 72020 24 1560143 5 231411601425514520116014032 2 3 44 3 2 2 4 4 44 3 2 2 4 4 3 2 2 34 3 2 2 3 4 3 2 2 3 44 3 2 2 3m n mn nm m n m n n m nm m n m n n m m n m n mnm m n m n mn n m n m n mn nm m n m n mn n + + + ++++ + + + = + + 44 3 2 2 351414116014= + + m m n m n mn 34. 13.13.13.13.13.1213341625145121338121312730141338124 9125 12301 241338121312730141340 381213127301413381213127301413378x yy zz mm n x y z m nx y z m n x y z m nx y z m n x y z m n++ + + + ++++ + + += + + + + = + +14.14.14.14.14.5612352338538341623112411212152331639403111123820 9246 9 2124 1624 15 3940165 22 93311 2424121216 9926411241123604015233112411212152334 324 3 2 4 3 23 4 34 3 2 4 24 3 2 4 3 2a a aa aa a a a a aa a a aa a a a a aa a a a a a a+ + + ++ + + + + ++ + + += + = + =. +13241211172644 2a a.EJERCICIO 301.1.1.1.1. x xx x xxRta x x x3 23 23 253 5 63 63 11 + + + + + .4.4.4.4.4. x xx x xxRta x x x3 23 23 24 84 1354 13 + + + +.7.7.7.7.7. 5 8 114 8 115 8 113 2 33 33 23 2 3a ab ba ba abRta a ab b+ ++ + .2.2.2.2.2. + + + ++ + + +5 9 65 9 6 8 98 95 9 6 8 9a b ca b c xxRta a b c x.5.5.5.5.5. m mn nm m n mn nm nRta m m n mn n4 3 44 2 2 3 42 24 2 2 3 43 64 3 6 84 84 3 6 8 + + + + +.8.8.8.8.8.1213412134x yx y +3.3.3.3.3. a ba a b ab ba b ab bRta a a b ab b3 33 2 2 32 2 33 2 2 38 5 38 5 48 5 3 + + + .6.6.6.6.6. 4 5 5 25 4 84 9 64 5 5 23 2233 2x x xx xx xRta x x x+ + ++ .Rta x y.12134 35. 9.9.9.9.9. 5 7 85 7 8 115 7 8 12 22 22 2x xy yx xy yRta x xy y + + + + + +.10.10.10.10.10. nm m n mn nm m n mn nm m n mn nmRta m m n mn n33 2 2 33 2 2 33 2 2 333 2 2 39 8 59 8 5 210 8 5 210 8 5 2 + + + + + + .11.11.11.11.11. 05 85 8033 + + a aa aRta.EJERCICIO 311.1.1.1.1. ( )x x yx x yy = +=6.6.6.6.6. ( ) ( )a a b a ba a b a ba a a+ + += + += =211.11.11.11.11. ( ) ( )x y x y z x y zx y x y z x y zx y z+ + + + = + + + += + 22.2.2.2.2. ( )x x xx x xx2 22 23 53 53 5+ += += +7.7.7.7.7. a b a a ba b a a ba a a2 2 2 2 22 2 2 2 22 2 2223 2+ + = + += =12.12.12.12.12. ( ) ( ) ( )a b a a b a ba b a a b a bb + + + += + + = 2223.3.3.3.3. ( )a b aa b aa b+ += + + = + 2 32 33 38.8.8.8.8. { } { }2 1 32 1 31 3 4a x a a xa x a a x + + = + + += + =13.13.13.13.13. ( ) ( ) [ ] + + + += + + + + = + +x y xy x xy y xyx y xy x xy y xyx xy y2 2 2 22 2 2 22 22 32 33 3 24.4.4.4.4. ( )4 24 26m m nm m nm n = + += +9.9.9.9.9. ( ) [ ]x y x xy y x yx y x xy y x yx xy y2 2 2 2 2 22 2 2 2 2 22 2222+ + + + += + += +14.14.14.14.14. [ ] { } ( )8 2 3 38 2 3 38 42 2 2 2 22 2 2 2 22 2x xy y x xy y x xyx xy y x xy y x xyx y+ + + = + + + += +5.5.5.5.5. ( )2 3 4 32 3 4 32x y x yx y x yx+ += + = 10.10.10.10.10.( ) ( ) + + + = + + = +5 6 5 65 6 5 66 5m mm mm15.15.15.15.15. ( ) ( ) ( ) ( ) + + + + += + + +=a b a b b a a ba b a b b a a b330EJERCICIO 321.1.1.1.1. ( )[ ][ ]2222a a a ba a a ba a a ba b+ += + = + = 2.2.2.2.2. ( )[ ][ ]3 23 23 24x x y x yx x y x yx x y x yx + += + = + +=3.3.3.3.3. ( ) ( )[ ][ ]2222 2m m n m nm m n m nm m n m nm n += = + + += + 36. 4.4.4.4.4. ( ) ( ) ( )[ ][ ]4 3 2 34 3 2 34 3 2 36 3 42 2 2 2 22 2 2 2 22 2 2 2 22 2x x xy y xy x yx x xy y xy x yx x xy y xy x yx xy y+ + + += + + + + = + + + = + 5.5.5.5.5. ( ) ( ){ }{ }a a b a b c aa a b a b c aa a b a b c aa c+ + + += + + + + += + + + += +2226.6.6.6.6. ( )[ ] ( )[ ][ ] [ ]4 2 3 4 2 14 2 3 4 2 14 2 3 4 2 15 2m m n n mm m n n mm m n n mn + + += + + = + = +7.7.7.7.7. { }( )[ ]( )[ ][ ]2 5 22 5 22 5 22 5 22x x y x yx x y x yx x y x yx x y x yx y+ + += + += + + + = + + = +8.8.8.8.8. ( )[ ]{ }[ ]{ }{ }x xy y x xy yx xy y x xy yx xy y x xy yx xy y x xy yx xy y2 2 2 22 2 2 22 2 2 22 2 2 22 27 3 27 3 27 3 27 3 22 4 3 + + + = + + = + = + + + += + +9.9.9.9.9. ( ) ( ){ }[ ]{ }[ ][ ] + + + + += + + + += + + + + = + + + = a b a b a b a b aa b a b a b a ba b a b a b a ba b a b a b a ba b3 2 2222210.10.10.10.10. ( ) ( )[ ]{ }[ ]{ }{ } + + + += + + + = + + = + + + + += +x y x y x y x yx y x y x y x yx y x y x y x yx y x y x y x yx y4 24 24 24 2311.11.11.11.11. ( ) ( ) ( ) ( )[ ][ ] + + + + + + = + + + = + + = a b a b a b b a ba b a b a b b a ba b a b a b b a ba b2 32 32 33 712.12.12.12.12. ( ) ( )[ ]{ } ( )[ ]{ }{ }7 3 5 3 2 37 3 5 3 2 37 3 5 3 2 37 3 5 3 2 37 2 52 2 22 2 22 2 22 2 22m m n n m nm m n n m nm m n n m nm m n n m nm n + + += + + + = + + = + + + + = + 13.13.13.13.13. ( ) ( ) ( )[ ]{ }[ ]{ }{ }2 4 42 4 46 46 4a a b a b a b aa a b a b a b aa b a b a b aa b a b a b ab + + += + + + = + += + + =14.14.14.14.14. ( ){ } ( )[ ]( ){ }[ ]( )[ ]( )( )3 5 2 63 5 2 63 5 2 63 5 2 63 5 2 65 5 6x y x y x x yx y x y x x yx y x y x x yx y x y x x yx y x y x x yx y + + + += + + + = + + + = + + = + + + += +15.15.15.15.15. ( ) ( ) ( ){ }[ ]{ }[ ][ ]6 2 2 26 2 2 26 2 2 26 2 2 26 7c a c a c a a c cc a c a c a a c cc a c a c a a c cc a c a c a a c ca c + + + + += + += += + + + + + + + = +16.16.16.16.16. ( ) ( )( ){ } ( )[ ]( ){ }[ ]{ }[ ][ ] + + + += + + + = + + + = + + = + + + += + +3 2 2 2 5 63 2 2 2 5 63 2 2 2 5 63 2 2 2 5 63 2 2 2 5 66 2 1m n m m m n nm n m m m n nm n m m m n nm n m m m n nm n m m m n nm n 37. 17.17.17.17.17. ( ) ( )( )[ ] ( ){ }( )[ ]{ }[ ]{ }{ }2 5 3 2 42 5 3 2 42 5 3 2 42 5 3 2 42 5 3 2 45 6a b a c a b c a ba b a c a b c a ba b a c a b c a ba b a c a b c a ba b a c a b c a ba b+ + + + + += + + + + + = + + + + + + + = + + + + = + + + = 18.18.18.18.18. ( )( )[ ] ( ) ( ) ( ){ }( )[ ] { }[ ] + + + + + += + + + + = + + = + + = 3 2 3 2 3 23 2 3 2 3 23 2 3 2 3 23 2 3 4 2 14x x y x y x x yx x y x y x x yx x y x y x x yx x y x y19.19.19.19.19. ( )[ ] ( )[ ] [ ] ( )[ ]{ }[ ] [ ] [ ]{ }{ } + + + + = + = + + += +=a a b c ca a b c ca a b c cb c cb20.20.20.20.20. ( )[ ]{ } ( )[ ]{ } ( )[ ]{ } [ ]{ }{ } { } + + += + + = + + = = a b b a a ba b b a a ba b b a a ba b b a a ba b3 321.21.21.21.21. ( )[ ]{ } ( )[ ]{ } ( ){ }[ ][ ]{ } [ ]{ } { }[ ]{ } { } [ ] + + + + + = + + + + = + + + += + + + + += + +a b c c a b a ba b c c a b a ba b c c a b a ba b c c a b a ba b c222.22.22.22.22. ( )( ){ } ( ) ( ){ }[ ]( ){ } { }[ ]{ }[ ][ ] + + + + + += + + += + + + += + + += + + + + + = + 3 4 2 33 4 2 33 4 2 33 4 2 33 4 2 32 4 7m m n m m n nm m n m m n nm m n m m n nm m n m m n nm m n m m n nm n23.23.23.23.23. ( ) ( ) ( )[ ]{ }[ ][ ]{ }[ ]{ }[ ][ ] + + + + = + + + = + + + + = += + + = x x y x y z x y yx x y x y z x y yx x y x y z x y yx x y zx x y z y z22 224.24.24.24.24. ( ) ( ) ( )[ ]{ }[ ][ ]{ }[ ]{ }[ ][ ] + + + += + + + += + = = + +a a a b a b c a ba a a b a b c a ba a c a ba a c a b a b c3EJERCICIO 331.1.1.1.1.( )a b c da b c d + = + + 2.2.2.2.2.( )x xy yx xy y2 22 23 63 6 += + +3.3.3.3.3.( )x x xx x x3 23 24 3 14 3 1+ += + +4.4.4.4.4.( )a a b ab ba a b ab b3 2 2 33 2 2 35 35 3 + = + + 5.5.5.5.5.( )x x x xx x x x4 3 24 3 22 2 12 2 1 + += + +6.6.6.6.6.( )22a b c da b c d+ += + 7.7.7.7.7.( )x x xx x x3 23 23 43 4+ + = +8.8.8.8.8.( )x x y xy yx x y xy y3 2 2 33 2 2 35 35 3 + = +9.9.9.9.9.( )a x xy ya x xy y2 2 22 2 222 = + +10.10.10.10.10.( )a b bc ca b bc c2 2 22 2 222+ = + + 38. EJERCICIO 341.1.1.1.1. ( )( )[ ]x y x yx y x y+ + = 222.2.2.2.2. ( ) ( )( ) ( )[ ]4 2 3 24 2 3 2m n m n m nm n m n m n + + + = + + 3.3.3.3.3. ( )[ ]( )[ ]{ }x xy x xy yx xy x xy y2 2 22 2 233 + += +4.4.4.4.4. [ ] ( )[ ] ( )[ ]x x x x xx x x x x3 23 23 4 2 3 2 33 4 2 3 2 3 + + += + + + +5.5.5.5.5. ( )[ ]{ }( )[ ]{ }[ ]2 3 22 3 2a b a a b aa b a a b a+ + + = + + + EJERCICIO 356.6.6.6.6. ( )( )[ ] + += +2 32 3a a ba a b7.7.7.7.7. ( ) ( )( ) ( )[ ]2 32 32 2 2 22 2 2 2x xy y xy x yx xy y xy x y+ + + += + + +8.8.8.8.8. x x xx x x3 23 23 4 23 4 2 + = + + { }9.9.9.9.9. ( )[ ] ( )( )[ ] ( ){ }m m m mm m m m4 24 23 2 3 2 33 2 3 2 3 + + + += + + +1.1.1.1.1. 2 3 6 = 2.2.2.2.2. =4 8 323.3.3.3.3. = 15 16 2404.4.4.4.4. ab ab a b a b = = + +1 1 1 1 2 25.5.5.5.5. 2 3 6 62 2 1 3x x x x = =+6.6.6.6.6. = =+ +4 4 42 2 2 1 1 2 3 3a b ab a b a b7.7.7.7.7. = =+ +5 5 53 2 3 1 1 2 4 3x y xy x y x y8.8.8.8.8. a b a x a b x a b x2 3 2 2 2 3 4 33 3 3 = =+9.9.9.9.9. = =+4 5 20 202 2 2 1 2 3 2m mn p m n p m n p10.10.10.10.10. 5 6 302 2 2 2a y x a x y = 11.11.11.11.11. = =+x y y z x y z x y z2 3 3 4 2 3 3 4 2 6 44 4 412.12.12.12.12. abc cd abc d abc d = =+1 1 213.13.13.13.13. = =+15 16 240 2404 3 2 3 2 4 3 3 2 7 3x y a x a x y a x y14.14.14.14.14. 3 4 122 3 2 2 3 2a b x y a b x y = 15.15.15.15.15. 3 7 21 212 3 5 2 1 3 1 5 2 4 6a bx b x a b x a b x = =+ +16.16.16.16.16. = =+8 9 72 722 3 2 4 2 2 1 3 4 2 3 3 4m n a mx a m n x a m n x17.17.17.17.17. a b ab a bm n m n = + +1 118.18.18.18.18. = + +5 6 302 3 2 3a b a b x a b xm n m n19.19.19.19.19. x y c x y c x y c x y cm n m n x m m n n x m n x = = + + + +1 2 2 120.20.20.20.20. = + +m n m n m nx a x a6 62 2 1EJERCICIO 361.1.1.1.1. a a a am m m m m = =+ + + +1 1 2 12.2.2.2.2. = =+ + + +x x x xa a a a a2 2 2 23.3.3.3.3. 4 4 41 1 1 1 2 1a b ab a b a bn x x n x x n x = = + + + + + +4.4.4.4.4. = = + + + + + + + + + +a b a b a b a bn n n n n n n n n n1 2 2 1 2 2 2 3 2 25.5.5.5.5. =+ + + + + +3 4 124 1 2 3 2 6 2 4a b a b a bn n n n n n6.6.6.6.6. 3 4 12 122 3 1 2 2 1 3 2 3 5x y x y x y x ym m m m m m = =+ + + + + + + +7.7.7.7.7. 4 5 202 4 5 1 2 7 2 5x b x b x ba a a a a a+ + + + + + = 8.8.8.8.8. a b c a b a b c a b cm n m n m m n n m n = = + +2 2 2 39.9.9.9.9. =+ + x y x y c x y cm a m a m a1 2 3 5 2 2 2 2 3 24 410.10.10.10.10. = 5 7 351 2 3 4 3 3 2 5m n c m n m n ca b a b a b 39. EJERCICIO 371.1.1.1.1.12451245410252 3 5 5 5a a b a b a b a b = = =2.2.2.2.2. = = =377143771421983142 2 32 5 2 5 2 5m n a ma m n a m n a m n3.3.3.3.3.2335615252 3 2 4 2 6 4 2 6 4x y a x y a x y a x y = = 4.4.4.4.4. = =18454401103 4 3 2 3 5 5 3 5 5m n a m n a m n a m n5.5.5.5.5. = = 78271456143 4 4abc a a bc a bc6.6.6.6.6. = =355636123 4 2 5 2 3 9 2 3 9x y a by a bx y a bx y7.7.7.7.7.1335315151 1a a a am m m = =+ +EJERCICIO 388.8.8.8.8. = =+ +342532153103 1 3 1 3a ab a b a bm m m9.9.9.9.9.5631012121421 2 1 2a b ab ca b c a b cm nm n m n = = + + + +10.10.10.10.10. = =+ + +293523152151 12 1 2 1 2 1 2 1a b a ba b a bx m x mx m x m11.11.11.11.11.384512403102 3 2 3 2a b a b a b a bm n m n m n m n = = 12.12.12.12.12. = =+ 211447247871 3 2 3 22 2 1 2 2 2 1 2a b c a ba b c a b cx x xx x x x1.1.1.1.1. a a a a a = = + +3 3 32 1 1 2 42.2.2.2.2. 3 3 32 3 2 2 2 3 1 2 6x x y a x a x y a x y = =+ +3.3.3.3.3. = =+ + +m n m mn m n m n2 2 3 2 2 1 1 3 5 43 5 15 154.4.4.4.4. 4 5 20 202 3 2 2 2 3 1 2 2 6 2 2a a x ay a x y a x y = =+ +5.5.5.5.5. = = + + + + +a ab a b a b a bm x m x m x2 3 6 62 1 2 1 3 16.6.6.6.6.122335630153 2 4 2 4 3 1 6 4x a x a m a x m a x m = =+ +7.7.7.7.7.233431812322 4 4 12 4 4 1 6 5a a b a ba b a bm xm x m x = = ++ + + + + +EJERCICIO 398.8.8.8.8. = = + + + + +35511015503103 22 3 1 2 4m a m a ma m a mx ax a x a9.9.9.9.9. 2 3 4 24 242 3 1 2 3 1 7a a a a a a = =+ + +10.10.10.10.10. = = + + + +3 4 560 602 3 23 1 2 2 1 1 6 4b a b ab a xa b x a b x11.11.11.11.11. a b a ab a xa b x a b xm xm x m x = = + + + + + +2 22 1 2 1 5 12 36 612.12.12.12.12. = =+ + + + +12351033468342 2 3 22 1 3 2 1 2 1 8 4x y xy x x yx y x y1.1.1.1.1. 326 23 24 3x xxx x +2.2.2.2.2. 8 3216 62 235 3 2x y yaxax y ax y3.3.3.3.3. x xxx x x23 24 322 8 6 + + 4.4.4.4.4. a a aaba b a b a b3 24 3 24 633 12 18 + + 40. 5.5.5.5.5. a ab baba b a b ab2 23 2 2 322 + + 6.6.6.6.6. x x xa xa x a x a x5 32 22 7 2 5 2 36 833 18 24 7.7.7.7.7. m m n nm xm x m n x m n x4 2 2 437 5 2 3 43 744 12 28 + + 8.8.8.8.8. x x y xyax yax y ax y ax y3 2 236 5 2 4 34 64 6 + +9.9.9.9.9. a a b aba ma m a bm a b m3 2 24 27 2 6 2 5 2 25 844 20 32 + +10.10.10.10.10. a a aaa a aa a am m mm m mm m m + + = + + + ++ 1 21 1 1 2 11 122 2 22 2 211.11.11.11.11. x x xxx x xm m mmm m m+ + + + 1 123 1 3 3 1333 9 312.12.12.12.12. a b a b a ba ba b a b a bm n m n m nm n m n m n+ + + ++ + + + +1 1 2 222 1 1 2 333 3 3EJERCICIO 4013.13.13.13.13. x x xxx x x x3 225 4 3 23 5 644 12 20 24 + + +14.14.14.14.14. a a x a xbxa bx a bx a bx bx4 3 2 234 3 3 4 2 5 36 9 833 18 27 24 + + 15.15.15.15.15. a a a aa xa x a x a x a xn n n nnn n n n+ + ++ + + + + +3 2 122 3 2 2 2 2 2 1 2 2 23 43 416.16.16.16.16. x x x xa xa x a x a x a x a x4 3 22 32 7 2 6 2 5 2 4 2 36 8 7 533 18 24 21 15 + + + + 17.17.17.17.17. + + 3 5 7 4515 25 35 203 2 2 32 22 4 2 2 3 3 2 2 4 2 5x x y xy ya xya x y a x y a x y a xy18.18.18.18.18. x x x xxx x x xa a a aa a a a+ + + ++ + + + + + +5 4 3 127 6 5 33 522 6 2 1019.19.19.19.19. a a b a b a b ba ya y a b y a b y a b y a b y8 6 2 4 4 2 6 83 211 2 9 2 2 7 4 2 5 6 2 3 8 23 355 15 5 15 5 + + + + 20.20.20.20.20. a b a b a b a ba ba b a b a b a bm n m n m n m nmm n m n m n m n+ ++ + + + ++ + + +344 12 4 41 2 2 4 3 632 3 2 1 5 2 2 7 2 3 91.1.1.1.1.1223252104151541521 2 23 2a baa a ba a b= +2.2.2.2.2.23342349612491233 1 3 1 14 3 2a ba ba b a ba b a b += ++ +3.3.3.3.3.35162553151551810155182321 1 2 2 2 12 2 2 3a b caca c abc aca c abc ac + + = + + +4.4.4.4.4.251329365336965232 222 2 2 1 2 24 3 2 2a ab ba xa x a bx a b xa x a bx a b x+ + = + + + 41. 5.5.5.5.5.1325143236610381235382 232 3 3 1 2 32 3 4 5x xy yyx y xy yx y xy y = + +6.6.6.6.6. 3 5 63109101510181091032952 32 1 3 2 3 2 33 3 2 3 2 3a b ca xa x a bx a cxa x a bx a cx + + = + +7.7.7.7.7.2913376633732122137174 2 2 43 44 3 4 2 3 2 4 3 4 47 4 5 6 3 8x x y yx yx y x y x yx y x y x y + += ++ + + +EJERCICIO 418.8.8.8.8.1213141558516524532540516524532182 2 2 222 2 2 2 2 2 2 24 2 2 2 2 2 2a b x ya ma m a b m a mx a mya m a b m a mx a my + + += + ++9.9.9.9.9.23125619346123815243361238581123 2 2 32 33 2 3 2 2 1 3 1 2 2 3 2 3 35 3 4 4 3 5 2 6m m n mn nm nm n m n m n m nm n m n m n m n+ + = + + + + + + +10.10.10.10.10.251335110571035521153557027521371146 4 2 2 4 63 4 33 6 4 3 3 4 4 2 3 3 2 4 4 3 3 4 6 33 10 3 3 8 5 3 6 7 3 4 9x x y x y ya x ya x y a x y a x y a x ya x y a x y a x y a x y + + += + ++ + + + + +1.1.1.1.1. aaa aaa a++ + 31332 3223.3.3.3.3. xxx xxx x++ + 5454 2020225.5.5.5.5. + + + +xxx xxx x3535 158 15227.7.7.7.7. 3 226 43 26 2222 2x yx yx xyxy yx xy y++ 2.2.2.2.2. aaa aaa a+ 31332 3224.4.4.4.4. mmm mmm m + +6565 3011 30226.6.6.6.6. ++ ++ +aaa aaa a2323 65 6228.8.8.8.8. 5 43 215 1210 815 22 8222 2x yx yx xyxy yx xy y + ++ + 42. 9.9.9.9.9. 5 735 715 215 8 21222 2a ba ba abab ba ab b++ + 11.11.11.11.11. + ++ + a ba ba abab ba ab b8 48 84 48 12 4222 213.13.13.13.13. ++ + + + +9 86 454 4836 3254 12 32222 2m nm nm mnmn nm mn n10.10.10.10.10. 7 32 414 628 1214 22 1222xxx xxx x++ + 12.12.12.12.12. 6 56 56 56 11 5222 2m nm nm mnmn nm mn n + +14.14.14.14.14. + + + +7 32 1114 677 3314 71 3322yyy yyy yEJERCICIO 421.1.1.1.1. x xy yx yx x y xyx y xy yx y2 23 2 22 2 33 3+ ++ + 5.5.5.5.5. a a aaa a aa a aa a a3 24 3 23 24 212+ + + +9.9.9.9.9. m m mam aam am am amam am am aam am a3 24 3 23 242222 + + + + + 2.2.2.2.2. a ab ba ba a b aba b ab ba a b ab b2 23 2 22 2 33 2 2 32223 3 + + + + 6.6.6.6.6. m m n nm nm m n m nm n m n nm n4 2 2 42 26 4 2 2 44 2 2 4 66 6+ ++ + 10.10.10.10.10. 3 5 24 512 20 815 25 1012 35 33 102 23 2 22 2 33 2 2 3a ab ba ba a b aba b ab ba a b ab b + + + + 3.3.3.3.3. a ab ba ba a b aba b ab ba a b ab b2 23 2 22 2 33 2 2 32223 3+ +++ ++ + ++ + +7.7.7.7.7. x x xxx x x xx x xx x x3 24 3 23 24 32 3 12 32 4 6 23 6 9 32 7 3 + + + + + + 11.11.11.11.11. 5 3315 9 35 315 5 9 3 34 2 2 45 3 2 44 2 3 55 4 3 2 2 3 4 5m m n nm nm m n mnm n m n nm m n m n m n mn n + + + + + 4.4.4.4.4. x xxx x xx xx x x3 24 33 24 23 1333 9 39 3 ++ ++ + + +9.9.9.9.9. 3 6 523 6 56 12 103 5 12 10325 3 235 2y yyy y yy yy y y ++ ++ ++ +12.12.12.12.12. a aa aa a aa a aa aa a a224 3 23 224 21112 1+ + + + 43. 13.13.13.13.13. x x xx xx x xx x xx x xx x x3 225 4 34 3 23 25 222 522 4 25 10 512 5+ ++ ++ + + 19.19.19.19.19. x xy yx xy yx x y x yx y x y xyx y xy yx x y xy y2 22 24 3 2 23 2 2 32 2 3 44 3 3 423223 6 33 5 3 + + + + + ++ + + +14.14.14.14.14. m m n mnm mn nm m n m nm n m n m nm n m n mnm m n m n mn3 2 22 25 4 3 24 3 2 2 33 2 2 3 45 4 2 3 43 22 83 22 6 48 24 165 20 16 + + + + + 20.20.20.20.20. n nnn n nn nn n n224 3 224 32 1122 12 2 1 + + + + 15.15.15.15.15. x xx xx x xx x xx xx x x224 3 23 224 21112 1+ + + + 21.21.21.21.21. a a b aba b ab ba b a b a ba b a b a ba b a b aba b a b a b ab3 2 22 2 35 4 2 3 34 2 3 3 2 43 3 2 4 55 4 2 2 4 53 42 103 42 6 810 30 405 22 40 + + + + + 16.16.16.16.16. x xx xx x xx x xx xx x x x x4 226 4 25 34 26 5 3 23 22 33 22 6 43 9 62 6 7 4 6 + + + + + + + +22.22.22.22.22. 8 12 6 92 316 24 12 1824 36 18 2716 24 273 2 2 34 3 2 2 33 2 2 3 44 2 2 4x x y xy yx yx x y x y xyx y x y xy yx x y y + + + + + 17.17.17.17.17. m m mmm m m mm m mm m m m m3 236 5 4 33 26 5 4 24 1144 14 4 1+ ++ + + + + 23.23.23.23.23. 2 3 42 54 6 2 810 15 5 204 4 13 3 203 24 3 23 24 3 2y y yyy y y yy y yy y y y + + + + + + 18.18.18.18.18. a aa aa a aa a aa aa a a a325 3 24 235 4 25 255 25 25 25 107 27 10 + + + + + + + +24.24.24.24.24. + + + ++ + + + a ax xa ax xa a x a xa x a x axa x ax xa a x a x ax x3 2 32 25 3 2 2 34 2 3 43 2 4 55 4 3 2 4 52 32 32 4 63 6 92 32 3 5 11 3 44. 25.25.25.25.25. x x y x y xyx xy yx x y x y x yx y x y x y x yx y x y x y xyx x y x y xy4 3 2 2 32 26 5 4 2 2 35 4 2 3 3 2 44 2 3 3 2 4 56 5 2 4 53 23 23 23 22 3 + + + + + + 30.30.30.30.30. y yy yy y yy y yy yy y y y y24 26 5 44 3 226 5 4 32 12 222 4 22 4 22 4 4 2 + + + + + + + +26.26.26.26.26. a a aa aa a a aa a a aa a aa a a a3 236 5 4 34 3 23 26 5 25 2 32 75 2 32 10 4 67 35 14 215 31 8 21 + + + + + + + +31.31.31.31.31. m mm mm m mm m mm mm m m m m m4 237 5 35 34 27 5 4 3 23 43 2 13 9 122 6 83 43 11 18 3 8 4 + + + + + + + + +27.27.27.27.27. m m mm mm m m mm m m mm m mm m m m4 3 226 5 4 25 4 34 3 26 5 332 332 2 2 63 3 3 95 6 9+ + ++ + + + + + + +32.32.32.32.32. a a aa a aa a a aa a a aa a a aa a aa a a a a a3 23 26 5 4 35 4 3 24 3 23 26 5 4 3 212 12 2 2 212 2 3 2 1+ ++ + ++ + + + + + + 28.28.28.28.28. a a b a b ab ba ab ba a b a b a b a ba b a b a b a b aba b a b a b ab ba a b a b a b ab b4 3 2 2 3 42 26 5 4 2 3 3 2 45 4 2 3 3 2 4 54 2 3 3 2 4 5 66 5 4 2 3 3 5 63232 2 6 2 234 6 3+ + ++ + + + + + + + +33.33.33.33.33. 8 12 63 2 424 36 18 316 24 12 232 48 24 424 52 38 33 26 43 2 2 32 25 4 3 2 2 34 3 2 2 3 43 2 2 3 4 55 4 3 2 2 3 4 5x x y xy yx xy yx x y x y x yx y x y x y xyx y x y xy yx x y x y x y xy y + + + + + + + + +29.29.29.29.29. x x y x y xy yx xy yx x y x y x y x yx y x y x y x y xyx y x y x y xy yx x y x y x y xy y4 3 2 2 3 42 26 5 4 2 3 3 2 45 4 2 3 3 2 4 54 2 3 3 2 4 5 66 4 2 3 3 2 4 5 622 2 2 2 22 2 2 3 2 + ++ + ++ + + + + + + 34.34.34.34.34. 5 4 2 3 12 25 4 2 310 8 4 6 210 8 4 6 25 4 8 5 5 2 6 6 24 3 24 28 7 6 5 46 5 4 3 24 3 28 7 6 5 4 3 2a a a aa aa a a a aa a a a aa a a aa a a a a a a a + + + + + ++ + + + + 45. 35.35.35.35.35. x x x xx x xx x x x xx x x x xx x x x xx x x xx x x x x4 3 23 27 6 5 4 36 5 4 3 25 4 3 24 3 27 6 5 212 3 62 2 2 2 23 3 3 3 36 6 6 6 63 6 3 6 + + + + + + + + + + ++ + + + + +40.40.40.40.40. 3 6 2 3 23 4 53 6 2 3 29 18 6 9 612 24 8 12 815 30 10 15 103 15 14 28 47 28 23 105 3 24 29 7 6 5 47 5 4 3 26 4 3 25 3 29 7 6 4 3 2a a a aa a aa a a a aa a a a aa a a a aa a a aa a a a a a a + + + + + + + + + + + + + + + 36.36.36.36.36. 3 2 5 42 13 2 5 43 2 5 46 4 10 83 2 5 43 5 9 10 8 3 43 23 26 5 4 35 4 3 24 3 23 26 5 4 3 2a a aa a aa a a aa a a aa a a aa a aa a a a a a+ + ++ + + + ++ + + + + 41.41.41.41.41. a b ca b ca ab acab b bcac bc ca b bc c+ ++ ++ + + 2222 2 2237.37.37.37.37. 5 3 4 23 15 3 4 215 9 12 65 3 4 25 3 11 11 17 3 4 24 3 24 28 7 6 56 5 4 34 3 28 7 6 5 4 3 2y y y yy yy y y yy y y yy y y yy y y y y y y y + + + + + + + 42.42.42.42.42. x y zx y zx xy xzxy y yzxz yz zx xy y yz z+ ++ ++ + + + 22222 32222 2 238.38.38.38.38. m m n m n nm m n mn nm m n m n m nm n m n m n m nm n m n m n mnm n m n m n nm m n m n m n m n m n mn n4 3 2 2 43 2 2 37 6 5 2 3 46 5 2 4 3 2 55 2 4 3 3 4 64 3 3 4 2 5 77 6 5 2 4 3 3 4 2 5 6 72 3 43 52 3 43 6 9 125 10 15 202 3 45 14 20 13 9 20 4 + + + + ++ + + ++ + + + + 43.43.43.43.43. 2 3 522 3 52 3 54 6 102 5 3 102222 2 2x y zx y zx xy xzxy y yzxz yz zx xy xz y yz z + + + + + ++ + + +39.39.39.39.39. x x y x y yx x y xyx x y x y x yx y x y x y x yx y x y x y xyx x y x y x y x y xy6 4 2 2 4 65 3 2 411 9 2 7 4 5 69 2 7 4 5 6 3 87 4 5 6 3 8 1011 9 2 7 4 5 6 3 8 1032 332 6 2 23 9 3 35 8 6 5 3 + + + + + + + + +44.44.44.44.44. x xy xz y yz zx y zx x y x z xy xyz xzx y xy xyz y y z yzx z xyz xz y z yz zx xyz y z2 2 23 2 2 2 22 2 3 2 22 2 2 2 33 3 33 + ++ + + ++ + ++ + + + + 46. EJERCICIO 431.1.1.1.1. a a aaa a aa a aa ax x xx x xx x xx x+ ++ + ++ ++ ++ ++ ++2 13 2 12 1312.2.2.2.2. + ++ + + + + + + ++ + ++ + ++ + ++ + + +x x xx xx x xx x xx x x xn n nn n nn n nn n n n3 2 125 4 34 3 25 4 3 222233.3.3.3.3. m m m mm mm m m mm m m mm m m mm m m m ma a a aa a a aa a a aa a a aa a a a a+ + + + + ++ + ++ + + + + + + ++ + + + + + + +2 1 124 3 2 13 2 12 1 14 3 1 12 32 2 2 23 3 3 36 5 34.4.4.4.4. a a aa aa a aa a aa a a an n nn nn n nn n nn n n n+ +++ + ++ ++ + ++ ++ + + + + 2 112 3 2 2 2 12 2 2 1 22 3 2 2 2 1 23 23 23 24 25.5.5.5.5. x x xx xx x xx x xx x x x xa a aa aa a aa a aa a a a a+ ++ ++ + ++ + ++ + + + ++ + ++ +2 13 12 5 2 4 2 32 3 2 2 2 12 5 2 4 2 3 2 2 2 12222 4 22 3 4 26.6.6.6.6. a a aa aa a aa a aa a aa a a ax x xx x xx x xx x xx x x x ++ ++ + + + + ++ + 2 32 12 32 4 62 32 8 31 222 11 11 22 1 27.7.7.7.7. a a aa a aa a aa a aa a aa a a a ax x xx x xx x xx x xx x xx x x x x+ ++ ++ + + + 3 23 23 23 22 4 5 21 21 22 2 1 2 22 1 2 2 2 32 2 2 3 2 42 2 1 2 2 2 3 2 48.8.8.8.8. m m m mm m mm m m mm m m mm m m mm m m m m ma a a aa a aa a a aa a a aa a a aa a a a a a+ + + + + + ++ + + + + + + + + + + + ++ + + + +4 3 2 11 2 32 3 2 2 2 1 22 2 2 1 2 2 12 1 2 2 1 2 22 3 2 2 2 1 2 2 1 2 222222 2 49.9.9.9.9. x x x xx x xx x x xx x x xx x x xx x x xa a a aa a aa a a aa a a aa a a aa a a a + + + + + + + 1 2 3 41 2 32 2 2 3 2 4 2 52 3 2 4 2 5 2 62 4 2 5 2 6 2 72 2 2 3 2 4 2 72222410.10.10.10.10. a b a b a b a ba b a ba b a b a b a ba b a b a b a ba b a b a b a b a bn n n nn nn n n nn n n nn n n n n + + + + + + 1 2 2 3 3 42 2 42 3 2 1 4 2 2 5 2 3 62 2 5 2 3 6 2 4 7 2 5 82 3 2 1 4 2 2 5 2 4 7 2 5 8222211.11.11.11.11. a ba ba a ba b ba a b a b bx xm mm x m xx m m xm x m x x m m x++++ ++ + ++++ +12.12.12.12.12. a ba ba aba b ba ab a b bx nx nx nx n x n + +1 1111 1 47. 13.13.13.13.13. + + + + ++ + + + + ++ + + + 5 36 830 6 1840 8 245 330 46 5 23 32 2 2 1 23 1 3 2 3 35 1 5 5 15 5 1 5 25 1 5 2 5 35 1 5 5 1 5 2 5 3a a aa a aa a aa a aa a aa a a a am m mm m mm m mm m mm m mm m m m m14.14.14.14.14. x y x y x yx y x y x yx y x y x yx y x y x yx y x y x yx y x y xa x a x a xa x a x a xa x a x a xa x a x a xa x a x a xa x a x+ + + + ++ + + + + + +2 1 1 12 1 2 2 2 1 2 33 1 2 3 3 2 2 3 1 2 13 2 2 3 1 2 1 3 2 23 1 2 1 3 2 2 3 3 2 13 1 2 3 3 2 2 34 32 4 102 8 64 16 1210 40 302 4 28 a x a xy x y +2 2 3 3 2 130EJERCICIO 441.1.1.1.1.1213131216191416164 936161653616222 22 2a ba ba abab ba ab ba ab b++ = + 2.2.2.2.2. x yx yx xyxy yx xy yx xy yx xy y++ = + = + 25135613215561030134 25301030132130131371013222 22 22 23.3.3.3.3.12131423322629212343638268 27362 612381335368123813353623382 23 2 22 2 33 2 2 33 2 2 33 2 2 3x xy yx yx x y xyx y xy yx x y xy yx x y xy yx x y xy y + + + +++= + = + 4.4.4.4.4.14231432116142123832661162 382 181211658201211658532 23 2 22 2 33 2 2 33 2 2 33 2 2a ab ba ba a b aba b ab ba a b ab ba a b ab ba a b ab b + + + +++= + = + 48. 5.251312322610363425131245232261015 123045 20 48603 4622610330176076351101760762 22 24 3 2 23 2 2 32 2 3 44 3 2 2 3 44 3 2 2 3 44 3 2 2 3 4m mn nm mn nm m n m nm n m n mnm n mn nm m n m n mn nm m n m n mn nm m n m n mn n+ ++ ++ + ++ ++= + + = + + 7. + + + + ++ + + +++ += + + += + + +1213323223343694121332262966343 3627 4 41227 418663466191223186634191223182 22 24 3 2 23 2 2 32 2 3 44 3 2 2 3 44 3 2 2 3 44 3 2 2 3 4x ax ax ax ax ax a xax a x a xa x a x ax ax a x a x ax ax a x a x ax ax a x a x a9.141314123211015383638341401301401201201151201103860 312045 4 612090 3 81201 1201103863120471207912022011038214047120791201101103 225 4 3 24 3 23 25 4 3 25 4 3 2 5 4 3 2x x xx xx x x xx x x xx x xx x x x xx x x x x x x x x x+ ++ + ++ + + + ++ ++ ++= + + + = + + + 6.3814252132682445324112215682445682496 151202 18248 306045341211112016243860453412374023193045235 4 33 225 4 3 25 4 3 25 4 3 2x xx xx x xx x xx xx x x x xx x x x xx x x x x+ ++ ++ + + +++= + + + = + + + 8.2715121423562281201842121526104253051222821 80420105 112 20084010 5305122281014204178401530512114101420139280123 2 22 25 4 3 24 3 2 2 33 2 2 3 45 4 3 2 2 3 45 4 3 2 2 3 45 4 3 2 2 3x x y xyx xy yx x y x yx y x y x yx y x y xyx x y x y x y xyx x y x y x y xyx x y x y x y + + + + + ++++ +++= + += + +5124xy 49. 10.10.10.10.10.341225142323526122641521261226415212158541010586124 61232 40 22512010 16 756020 12012058121012297120101603 2 2 32 25 4 3 2 2 34 3 2 2 3 43 2 2 3 4 55 4 3 2 2 3 4 55 4 3 2 2 3m m n mn nm mn nm m n m n m nm n m n m n mnm n m n mn nm m n m n m n mn nm m n m n m n + + + + ++ + +++ ++ +++= + +14012058125699401016076584 5 5 4 3 2 2 3 4 5mn n m m n m n m n mn n = + + EJERCICIO 451.1.1.1.1. x x x por xx x x x3 2 25 4 211 1 11 0 11 1 11 1 11 1 0 1 1 + ++ + + + + = + 2.2.2.2.2. x x x por x xx x x x x x4 3 2 3 27 6 5 4 3 23 5 8 2 71 3 5 0 81 2 0 71 3 5 0 82 6 10 0 167 21 35 0 561 1 11 3 13 19 0 5611 3 13 19 56+ + + + + + + + + + + + + + + + + = + + + 3.3.3.3.3. a a b a b ab b por a ab ba a b a b a b a b ab b4 3 2 2 3 4 2 26 5 4 2 3 3 2 4 5 63 2 5 21 3 2 5 11 2 11 3 2 5 12 6 4 10 21 3 2 5 11 1 7 12 13 7 17 12 13 7+ + ++ + ++ + + ++ + + + + + = + + + 4.4.4.4.4. m m n mn n por m mn nm m n m n m n m n mn n3 2 2 3 3 2 36 5 4 2 3 3 2 4 5 65 6 41 5 6 11 0 4 11 5 6 14 20 24 41 5 6 11 5 2 20 19 10 15 2 20 19 10 + + + ++ + + + + + + = + + 5.5.5.5.5. x x por x xx x x x4 2 4 28 6 4 28 3 6 51 0 8 0 31 0 6 0 51 0 8 0 36 0 48 0 185 0 40 0 151 0 2 0 50 0 58 0 152 50 58 15 + + + + ++ + + + + ++ + + + + + + + + + + + = + 6.6.6.6.6. a a a por a a a aa a a a a a a6 4 2 8 6 4 214 12 10 8 6 4 23 6 10 4 3 21 0 3 0 6 0 101 0 4 0 3 0 21 0 3 0 6 0 104 0 12 0 24 0 403 0 9 0 18 0 302 0 6 0 12 0 201 0 7 0 9 0 23 0 52 0 42 0 207 9 23 52 42 20 + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + = + + + 50. 7.7.7.7.7. x x x por x xx x x x x9 6 3 6 315 12 9 6 34 3 2 3 8 101 0 0 4 0 0 3 0 0 23 0 0 8 0 0 103 0 0 12 0 0 9 0 0 68 0 0 32 0 0 24 0 0 1610 0 0 40 0 0 30 0 0 203 0 0 20 0 0 51 0 0 70 0 0 46 0 0 203 20 51 70 46 20 + ++ + + + + + + + + + + ++ + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + = + + 9.9.9.9.9. x x y x y x y y por x yx x y x y x y x y x y y5 4 3 2 2 3 5 2 27 6 5 2 4 3 3 4 2 5 73 6 4 2 41 3 6 4 0 12 0 42 6 12 8 0 24 12 24 16 0 42 6 8 20 24 18 0 42 6 8 20 24 18 4 + + + + + + + + = 11.11.11.11.11. n n n n por n nn n n n n n n n n6 4 3 4 210 8 7 6 5 4 3 23 5 8 4 3 41 0 3 5 0 8 41 0 3 0 41 0 3 5 0 8 43 0 9 15 0 24 124 0 12 20 0 32 161 0 6 5 13 23 8 44 12 32 166 5 13 23 8 44 12 32 16 + + ++ + + ++ + ++ + + + + + + + + + + + ++ + + + += + + + +13.13.13.13.13. x x y x y y por x x y x y y10 6 4 2 8 10 6 4 2 2 4 65 3 6 4 51 0 0 0 5 0 0 0 3 0 61 0 4 0 5 0 11 0 0 0 5 0 0 0 3 0 64 0 0 0 20 0 0 0 12 0 245 0 0 0 25 0 0 0 15 0 301 0 0 0 5 0 0 0 3 0 61 0 4 0 10 0 21 0 28 0 23 0 + ++ + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + 9 0 33 0 64 10 21 28 23 9 33 616 14 2 12 4 10 6 8 8 6 10 4 12 2 14 16x x y x y x y x y x y x y x y y14.14.14.14.14. a a a por aa a a a am m mm m m m m + + ++ + + + + + + = + + + 3 5 51 3 0 51 0 51 3 0 55 15 0 251 3 5 20 0 253 5 20 251 3 22 1 1 38.8.8.8.8. m m m por m m m mm m m m m m m12 8 4 16 12 8 428 24 20 16 12 8 47 9 15 5 9 4 31 7 9 151 5 9 4 31 7 9 155 35 45 759 63 81 1354 28 36 603 21 27 451 12 53 127 187 192 87 4512 53 127 187 192 87 45 + + + + + + + + ++ + + ++ + + + + = + + + 10.10.10.10.10. 6 4 6 2 2 76 0 0 4 6 21 0 2 1 76 0 0 4 6 212 0 0 8 12 46 0 0 4 6 242 0 0 28 42 146 0 12 2 36 6 16 38 44 146 12 2 36 6 16 38 44 145 2 4 29 7 6 5 4 3 2a a a por a a aa a a a a a a a + + + + + + + + + + + + + ++ + + + + + + ++ + + + += + + + +12.12.12.12.12. 3 4 5 33 4 0 0 11 0 5 33 4 0 0 115 20 0 0 59 12 0 0 33 4 15 29 13 0 5 33 4 15 29 13 5 34 3 4 3 2 37 6 5 2 4 3 3 4 6 7x x y y por x xy yx x y x y x y x y xy y + + + + + + + + + + ++ + + + + + = + + 15.15.15.15.15. a a a por a a aa a aa a a ax x x x x xx x xx x x x+ + + ++ + ++ + + + + + + + + + + + + + = + 2 1 1 3 12 5 2 4 2 32 2 2 1 2 2 15 7 7 61 5 0 77 0 6 17 35 0 496 30 0 421 5 0 77 35 6 78 5 42 77 35 678 5 42 7 51. 16.16.16.16.16. x x x por x x x xx x x xx x x xa a a a a a aa a a aa a a a+ + + + + + ++ + + ++ + + + + ++ + + + + + + + = + + 2 2 1 1 22 3 2 2 2 1 22 1 2 2 2 3 2 45 6 6 4 21 0 5 0 66 4 2 16 0 30 0 364 0 20 0 242 0 10 0 121 0 5 0 66 4 28 21 46 19 12 66 4 28 2146 19 12 617.17.17.17.17. a a a a por a a aa a a a a ax x x x x x xx x x x x x2 2 2 1 2 2 1 3 1 3 3 15 3 5 2 5 1 5 5 1 5 23 5 6 5 31 3 1 56 5 36 18 6 305 15 5 253 9 3 156 23 12 34 22 156 23 12 34 22 15+ + + + + + + + + + ++ + + = + + EJERCICIO 461.1.1.1.1. ( )( )4 5 34 2034 2012 604 8 6022a aaaa aaa a+ ++ + 2.2.2.2.2. ( )( )3 1 13 313 33 33 322 22 2 22 22 2 2a x xa x axa x a xa x aa x a+ ++ 3.3.3.3.3. ( )( )( )2 3 1 42 612 62 62 8 642 8 68 32 242 26 24223 223a a aaaa aaa aaa a aa aa a + + ++ ++ + +4.4.4.4.4. ( )( )( )x x xxxx xxx xxx x xx xx x x2 2 2224 224 226 4 24 26 4 21 1 11112 1122 11+ +++++ ++ ++ + + 5.5.5.5.5. ( )( )( )m m m mm mmm mm mm m mmm m mm m mm m m m + + ++ ++ + + +4 6 3 24646 2410 243 23 30 722 20 483 28 52 4823 223 24 3 23 24 3 26.6.6.6.6. ( )( )( )a b a ab b a ba ab ba ba a b aba b ab ba a b ab ba ba a b a b aba b a b ab ba a b ab b + + ++ ++ + + + + + + 2 22 23 2 22 2 33 2 2 34 3 2 2 33 2 2 3 44 3 3 422222 27.7.7.7.7. ( )( )( )3 2 1 1 13 6 313 6 33 6 33 9 9 313 9 9 33 9 9 33 6 6 323 24 3 23 24 3 25 4 3 24 3 25 4 2x x x x xx x xxx x xx x xx x x xxx x x xx x x xx x x x + + + + + + + + + + + 52. 11.11.11.11.11. ( )( )( )( )x x x xx xx xx x x xx xx x x xx xx x xx x xx xx x x x + + + + + + + + + + + +3 4 5 13 54 13 54 12 512 4 54 5124 4 485 5 603 21 43 602 22 224 3 23 224 3 212.12.12.12.12. ( )( )( )( )x x x x xx x xx xx x x x xx x xx x x x x x xx x xx x x x xx x x x xx x x x2 2 22 224 3 2 32 24 3 2 3 23 27 6 5 4 36 5 4 3 25 4 3 23 2 1 1 32 1 33 12 33 6 3 32 4 6 3 3 33 32 4 6 32 4 6 33 6 12 18 + + ++ + + + + + + + ++ + + + + ++ + + + + + + + ++ + +93 6 12 18 99 9 9 94 3 27 6 5 4 3 2xx x x xx x x x x x x13.13.13.13.13. ( )( )( )( )9 3 2 2 1 1 2 127 18 2 12 1 154 36 227 18 2 154 9 18 2 3 12 3 1108 18 36162 27 5454 9 18108 180 45 45 1823 24 3 23 24 3 2 226 5 45 4 34 3 26 5 4 3 2a a a a aa a aa aa a a aa a aa a a a aa aa a aa a aa a aa a a a a + + + + + + + ++ + 14.14.14.14.14. ( )( )a a b a b ba a ba b ba b a ba b a ba b a bx x x x x xx x xx x xx x x xx x x xx x x x+ + + ++ ++ ++ + ++ + ++ ++ ++ 1 2 1 22 1 21 2 23 2 2 1 2 22 1 2 2 3 43 2 3 48.8.8.8.8.( )( )( )x x x x xx xx xx x xx x xx xx x xxx x x xx x xx x x x x2 2224 3 23 224 25 3 24 25 4 3 21 1 21112 1222 2 4 22 4 5 2 + + ++ ++ + + + + + + + +9.9.9.9.9. ( )( )( )a a aaaa aaa a aaa a a aa a aa a a a aa am m mmmm mmm m mmm m m mm m mm m m m mm m + ++ + + + ++ + + 3 2 13232 62 3 612 3 63 2 63 3 2 631 112 1 12 1 112 1 3 2 2 2 12 1 12 1 3 2 2 2 13 2 2 1a a am m m2 2 12 3 6 +10.10.10.10.10. ( )( )( )a a a aa aaa aa aa a aaa a aa a aa a a a + + + + + 1 2 322 23 233 23 9 66 11 623 223 24 3 23 24 3 2 53. EJERCICIO 471.1.1.1.1. ( ) ( )4 3 5 24 12 5 109 22x xx xx+ + += + + += +2.2.2.2.2. ( ) ( ) ( )6 4 3 1 5 26 24 3 3 5 108 312 2 22 2 22x x xx x xx+ + + += + + += +3.3.3.3.3. ( ) ( ) ( )a a x a x a a x aa ax ax a ax aa ax + + = + + += +3 2 33 6 3102 2 224.4.4.4.4. ( ) ( )x y y x x yx y x x y y x yx y x y2 2 2 2 2 22 2 2 2 2 2 2 22 2 2 21 1 33+ + + = + + + = + +5.5.5.5.5. ( ) ( )4 5 3 34 5 3 3 3 33 3 23 2 2 2 2 2 23 2 4 2 2 3 24 3 2 2 2m mn m m n m m nm mn m m n m mnm m m n mn + + = + + += + + 6.6.6.6.6. ( ) ( ) ( )y x y y x y x y xy x y x y y x y y x y yy y2 2 3 3 2 2 2 2 22 2 3 2 3 3 2 2 2 2 2 23 21 1 13+ + + + = + + + += +7.7.7.7.7. ( ) ( )( )( )5 2 1 4 65 10 4 4 610 4 46 6222x x x xx x x x xx x x xx x+ + + = + + + + = + = +8.8.8.8.8. ( )( ) ( )( ) ( )( )( )a a a a aa a a a a a aa a aa a aa a+ + + += + + + += + = + += + +5 5 3 2 2 5 45 5 25 3 2 2 4 5 205 5 3 45 5 3 122 5 72 22 22 229.9.9.9.9. ( )( ) ( )( ) ( )( )( ) ( )a b a b a b a b a b a ba ab b a ab b a ab ba ab b a ab b a ab ba ab b+ + + = + = + + + + += + +4 3 5 2 3 3 64 3 15 2 3 3 64 3 15 2 3 3 614 5 52 2 2 2 2 22 2 2 2 2 22 210.10.10.10.10. ( ) ( )( )( ) ( )( )( )a c a ca c a c a c a ca ac ac c a ac ac ca ac c a ac ac cac+ = + + = + + + += + + + + =2 22 2 2 22 2 2 22411.11.11.11.11. ( ) ( )( )( ) ( )( )( ) ( )( ) ( )3 4 3 33 4 3 33 4 3 33 2 4 2 3 33 6 3 4 8 4 3 32 14 42 2 2 22 22 2 2 2 2 22 2 2 2 2 22 2 2 2 2 22 2x y x y x yx y x y x y x y x yx xy xy y x xy xy y x yx xy y x xy y x yx xy y x xy y x yx xy y+ + = + + + = + + + + + = + + + + = + + + + = + 12.12.12.12.12.( ) ( ) ( )( )( ) ( )( ) ( )( )( )m n m n m nm n m n m n m n m n m nm mn n m