EJ ERCI CI O 11.Unadeudaseexpresaensentido 1.Unadeudaseexpresaensentido 1.Unadeudaseexpresaensentido 1.Unadeudaseexpresaensentido 1.Unadeudaseexpresaensentidonegativo.Luegoinicalmenteelestado negativo.Luegoinicalmenteelestado negativo.Luegoinicalmenteelestado negativo.Luegoinicalmenteelestado negativo.LuegoinicalmenteelestadoeconmicodePedroes-60bs. econmicodePedroes-60bs. econmicodePedroes-60bs. econmicodePedroes-60bs. econmicodePedroes-60bs.Alrecibir320bs.Aumentasucapital Alrecibir320bs.Aumentasucapital Alrecibir320bs.Aumentasucapital Alrecibir320bs.Aumentasucapital Alrecibir320bs.Aumentasucapitaltantosbs.comoharecibido;entonces tantosbs.comoharecibido;entonces tantosbs.comoharecibido;entonces tantosbs.comoharecibido;entonces tantosbs.comoharecibido;entonceslaoperacinquedaexpresadacomo laoperacinquedaexpresadacomo laoperacinquedaexpresadacomo laoperacinquedaexpresadacomo laoperacinquedaexpresadacomoseindica seindica seindica seindica seindica + + 60 320 260 bs.2.2.2.2.2.1170 1 515 345 . . sucres3.3.3.3.3.200 56 189 67 + +$4.4.4.4.4. + + 665 1178 2280 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 0EJ ERCI CI O 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 42 8 8 0 88 45 8 20 12 11!!!amamam7.7.7.7.7. + + + + + 1 22 1 4 5 101 23 1 6 7 111 23 3 1 1 6 3 4 121 23 33 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 21654 61+ =+-=+!!longlat.11.11.11.11.11.- + =+ 75 135 60 aosEJ ERCI CI O 31.1.1.1.1.+ 32 16 m m ;2.2.2.2.2.+ 10 4 m 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. 4002 8004003 1 200 + m corredorm yo .7.Los40piesdelongituddelposte 7.Los40piesdelongituddelposte 7.Los40piesdelongituddelposte 7.Los40piesdelongituddelposte 7.Los40piesdelongituddelposteserepartenasi:15piesquesobresalen serepartenasi:15piesquesobresalen serepartenasi:15piesquesobresalen serepartenasi:15piesquesobresalen serepartenasi:15piesquesobresalen-seasumenensentidopositivo-. -seasumenensentidopositivo-. -seasumenensentidopositivo-. -seasumenensentidopositivo-. -seasumenensentidopositivo-.25piesqueseencuentranenterrados. 25piesqueseencuentranenterrados. 25piesqueseencuentranenterrados. 25piesqueseencuentranenterrados. 25piesqueseencuentranenterrados.-seasumenensentidonegativo-. -seasumenensentidonegativo-. -seasumenensentidonegativo-. -seasumenensentidonegativo-. -seasumenensentidonegativo-.Alintroducir3piesms,seadicionan Alintroducir3piesms,seadicionan Alintroducir3piesms,seadicionan Alintroducir3piesms,seadicionan Alintroducir3piesms,seadicionanalosqueestanbajoelsueloysedeben alosqueestanbajoelsueloysedeben alosqueestanbajoelsueloysedeben alosqueestanbajoelsueloysedeben alosqueestanbajoelsueloysedebendescontardelosqueestanporencima. descontardelosqueestanporencima. descontardelosqueestanporencima. descontardelosqueestanporencima. descontardelosqueestanporencima.Aritmticamentesignifica: Aritmticamentesignifica: Aritmticamentesignifica: Aritmticamentesignifica: Aritmticamentesignifica:

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( )( )( )( ) + + + + + +120 60 1 120 60 60120 60 2 120 120 0120 60 3 120 180 60120 60 4 120 240 120KmKmKmEJ ERCI CI O 7.1. 1. 1. 1. 1. x x x + 2 32.2.2.2.2.8 9 17 a a a + 3.3.3.3.3.11 9 20 b b b + 4.4.4.4.4. b b b 5 65.5.5.5.5. 8 9 mm m6.6.6.6.6. 9 7 16 m m m7. 7. 7. 7. 7. 4 5 9 a 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 x 1 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 23 a a a a + + 18.18.18.18.18.15 20 36 x x x x + + 19.19.19.19.19. 7 8 9 24 m 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 39 a 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 23 a 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 06 07 0 8 26 , , , , , 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. mm m m m m 8 7 3 2038.38.38.38.38. + + + + + +x x x x x xa a a a a a 1 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 abEJ ERCI CI O 81.1.1.1.1.8 6 2 a a a 2.2.2.2.2.6 8 2 a a a 3.3.3.3.3.9 15 6 ab ab ab 4.4.4.4.4.15 9 6 ab ab ab 5.5.5.5.5.2 2 0 a a 6.6.6.6.6. + 7 7 0 b b7.7.7.7.7. + 14 32 18 xy xy xy8.8.8.8.8. + 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 25 xy 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 17 mn mn mn17. 17. 17. 17. 17. 502 405 97 ab ab ab 18.18.18.18.18. + 1024 1018 6 x x x19.19.19.19.19. + 15 15 0 ab 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 31181128.28.28.28.28.34 56 224 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 2 a 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 a 1 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 bmn mn mn mn40.40.40.40.40.085 0 5 0 35 , , , mxy mxy mxy EJ ERCI CI O 91.1.1.1.1.9 3 5 11 a a a a + 2.2.2.2.2. + 8 9 0 x x x3.3.3.3.3.12 23 5 16 mn mn mn mn 4.4.4.4.4. + x x x 19 18 05.5.5.5.5.19 10 6 15 m m m m + 6.6.6.6.6. + 11 15 26 0 ab ab ab7.7.7.7.7. + 5 9 35 31 a 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 33030 y 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 a 8 9 1513.13.13.13.13.7 11 20 31 15 ab 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 xy 8 19 40 1216.16.16.16.16.7 21 80 53 ab 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 87 101 243 157 ax ax ax ax ax19. 19. 19. 19. 19. + 82 71 53 206 0 bx bx bx bx20.20.20.20.20.105 464 58 301 03 3 3 3a a a a + + 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 a 8 11 15 75 6426.26.26.26.26. + + + 7 21 14 30 82 80 c c c c c c27.27.27.27.27. + + mn mn mnmn mnmn 14 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 a 3 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 0 a a a a ax x x x x + 33.33.33.33.33. + + + + + + + +a a a a a ax x x x x x 1 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 9 b 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 28 a a a a a a a a + + + 40. 40. 40. 40. 40. + + 21 52 60 84 31 23 0 ab ab ab ab ab ab abEJ ERCI CI O 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 mn mmm m m nn 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 1411.11.11.11.11. m mn m mnm 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 06 07 0 9 3 3 30 3 0 6 3 2 7 0 4 07 3 3 3 0 5 09 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 b19.19.19.19.19. 0 4 313806250 21460 4252 250380 23 168148017506142 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 + ++ + + + +,,EJ ERCI CI O 11Para resolver los problemasdel 1 al 18 las literales toman los siguientes valores:a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/4 a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/4 a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/4 a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/4 a = 1 b = 2 c = 3 m = 1/2 n = 1/3 p = 1/41.1.1.1.1.3 3 1 2 6 ab 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

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_, 9.9.9.9.9.2 223 49 36 62 2bc 10. 10. 10. 10. 10. 4 12 412122 3 2 216 26 122 3 23 3m bc 11.11.11.11.11. mn a b 812138 1 2166486434 3 4 312.12.12.12.12. 434 132341829abc 13.13.13.13.13. 55 212131420141125112602 222b mnp

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14.14.14.14.14. 34233422333 842 932441836613232bc 15.15.15.15.15. 22121311911332 2mn

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17.17.17.17.17. 3 6423 642 32123 648729 3 373 248 372 2163 6 3 3 6 333 b cm.18.18.18.18.18. 35321253511423212521235443225023513212535325351526752252323 33 apbbmEJ ERCI CI O 12Para resolver los problemas del 1 al 18 las literales tomanlos 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+ +

_, + +

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+ + + + + a b da nEJ ERCI CI O 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 bc d + + 1 2 3 4 3 3 4 9 4 52.2.2.2.2. ( )( ) ( )( ) a bb a + + 1 2 2 1 3 1 33.3.3.3.3. ( )( ) b m c n a +

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_, 3 2 4 3 2 112141 1 12 14147.7.7.7.7. ( ) ( ) ( ) b c d a mn x2 2 2 2 562 2 3 4 112232 0 4 73 462876168 76161626 + + + + +

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+ 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 2 x 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 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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 + +EJ ERCI CI O 1717.17.17.17.17. 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 2EJ ERCI CI O 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+ + + + ++ + + + + + +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+ + ++ + ++ + + EJ ERCI CI O19Para 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 82 824 8 8 8 0x yx yx yy + + 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+ 60.60.60.60.60. 19451 40594069453 2 3 23 2 3 2 193 2a b a ba b a b a bEJ ERCI CI O 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+ + + + +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 64 727.27.27.27.27. 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 28EJ ERCI CI O 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 x13.13.13.13.13. 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 xEJ ERCI CI O 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 mam am a m a ma44 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 + + EJ ERCI CI O 241.1.1.1.1. 121413252 14132534132522 22 22 2aa ab ba ab ba ab b+ ++ + 2.2.2.2.2. 154523594523135 594523140945231559 + ++ + +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+ + ++++ + + + +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+ + + + + + EJ ERCI CI O 259.9.9.9.9. 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+ + + + + +++++ + + + + EJ ERCI CI O 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 51 2 61 2 3 2 1 52 64 3 81 10 24 24 11++ + + + + + + + + + + + 3.3.3.3.3. 1212531 221253121253121122533121 51 2 10272312aa 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 64 164 5 18 4 5 64 5 6 5256 8064 1816 25 24125 6 625256 5120 7 200 3000 3750 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 110121811012118121102122841012142510 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 51 2 312 21 4 5 8 316 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 91 111 2 9 1 2 21 22 36 8 7 + + + + 12.12.12.12.12. 16423563816423563816442345643843232063896 256 80 924231247789424 24 258xx xx x x + + + + + 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 515451255146415161645251252516 15 20 5 56+ + ++ + + + += + + + = + + += + + + =EJ ERCI CI O 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 mn pm n p mnpm 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 n13.13.13.13.13. + + + + + + + + + + +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+ ++ + + + + + + + +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+ + + + + + + + + + + + EJ ERCI CI O 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 98.8.8.8.8. 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 82 122 12.12.12.12.12. 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 44244 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 + +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 + + ++= + = + = 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 mn13.13.13.13.13. 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 xRtax x x+ + ++ . Rta x y .12134 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+ + += + += = 2 11.11.11.11.11.( ) ( ) 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 3 8.8.8.8.8.{ } { } 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 mnm mnmn = + += + 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 mm 15.15.15.15.15. ( ) ( ) ( ) ( ) + + + + += + + +=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 mn mnm mn mnmmn mnm n += = + + += +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 mn n mm mn 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 1mn m m m n nmn m m m n nmn m m m n nmn mm m n nmn mm m n nm n17. 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 b 3 321.21.21.21.21. ( ) [ ] { } ( ) [ ] { } ( ) { } [ ][ ] { } [ ] { } { } [ ]{ } { } [ ] + + + + + = + + + + = + + + += + + + + += + +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 c 222.22.22.22.22.( ) ( ) { }( ) ( ) { }[ ]( ) { } { }[ ]{ } [ ][ ] + + + + + += + + += + + + += + + += + + + + + = + 3 4 2 33 4 2 33 4 2 33 4 2 33 4 2 32 4 7m m n m mn nm m n m mn nm mn m mn nmmn m mn nmmn m mn 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 c 3EJERCICIO 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+ = + +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 mn mnm n mn mn + + + = + + 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 bmn m n =+ + 1 118.18.18.18.18. =+ +5 6 302 3 2 3a b a b x a b xmn m n19.19.19.19.19.x y c x y c x y c x ycmn mn x mmn 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 mm m = =+ + + + 1 1 2 12.2.2.2.2. = =+ + + +x x x xa a a a a 2 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 n 1 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 bcmn m n mmn n m n = =+ + 2 2 2 39.9.9.9.9. =+ + x y x y c x y cm a m a m a 1 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 bEJERCICIO 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 cmnm 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 bmn mn 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 + +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 mn+ + + ++ + + + +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+ + = + + +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 xy 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 + ++ + 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 nmnm 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 mamaam 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 nmnm 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+ + + + 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 11 325.25.25.25.25.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 + + + + + ++ + + + + 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 + ++ + + ++ + ++ + + + +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 22223 3.3.3.3.3. 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 xxx x xx x xx x xx x x x x+ ++ ++ + + + 3 23 23 23 22 4 5 21 2122 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 aaa a a aa a a aa a a aa a a a a a+ + + + + + ++ + + + + + + + + + + + ++ + + + +4 3 2 11 232 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 aaa a a aa a a aa a a aa a a a + + + + + + + 1 2 3 41 232 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 bab a b a b a ba b a b a b a bab 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 mmx m xx m mxmx m x x m mx++++ ++ + ++++ +12.12.12.12.12.a ba ba aba b ba ab a b bx nx nx nx n x n + +1 1111 113. 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 28a 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 + + + +++= + = + 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 + + + + + ++++ +++= + += + +5124xy10. 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 = + + EJ ERCI CI O 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 pora 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 porm 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 porx 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 pora 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 + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + = + + + 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 42 716. 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 6 17. 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+ + + + + + + + + + ++ + + = + + EJ ERCI CI O 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 + + + + + + + + + + + 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 m 2 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 2EJ ERCI CI O 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 mm 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 22 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.( ) ( ) ( )( )( ) ( )( ) ( )( )( )mn mn m nmn mn mn mn m n m nm mn n m mn n m mn nm mn n m mn nm mn n+ + + = + + + + + = + + + + + += + = +2 2 22 2 2 2 2 22 2 2 22 22 42 2 4 42 4 4 8 162 6 17 4 42 10 1613.13.13.13.13.( ) ( ) ( )( ) (