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8/9/2019 Gii PTVT bng PP lng lin hp
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Gii PTVT bng PP lng lin hpI.C s l thuyt
Cho hm s , xc nh trn .
Ta bit l nghim phng trnh .
M theo nh l Bzu nu l nghim ca a thc th
. T y ta c nhn xt:
Nu l mt nghim ca phng trnh th ta c th a phng trnh v
dng v khi vic gii phng trnh quy v gii phng trnh . Ta xtv d sau:II.Mt s v d
V d 1: Gii phng trnh: (HVKTQS 2000).
Gii: iu kin : .Ta thy l mt nghim ca phng trnh ( ta ngh n v khi v l nhng s
chnh phng) do ta c th a phng trnh v dng: nn ta bin i phng trnh nh
sau: , vn cn li ca chng ta l phi phn tch
ra tha s (Ch khi th ), v nh l Bzu ch pdng cho a thc nn ta phi bin i biu thc ny v dng c mt a thc, tc l ta a v
dng
iu ny gip ta lin tng n ng thc : nn ta bin
i :
.
Suy ra phng trnh n y ta ch cn gii phng
trnh:
.
Vy phng trnh cho c hai nghim v .Nhn xt: 1) Qua v d trn ta thy b cn thc ta s dng hng ng thc:
hai biu thc v ta gi l hai biu thc lin hp ca nhau. Nnphng php trn ta gi l phng php nhn lng lin hp.2) Vi phng php ny iu quan trng l ta phi bit c mt nghim ca phng trnh, t ta mi nhhng c cch bin i l xut hin nhn t chung. nhm nghim ta c th s dng my tnh b ti570MS hoc 570ES .
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V d 2: Gii phng trnh : (THTT).
Gii: iu kin : .
Nhn thy phng trnh trn vn c nghim nn ta ngh n cch gii phng trnh trn bng phngphp nhn lng lin hp.
8/9/2019 Gii PTVT bng PP lng lin hp
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Ta c:
Mt khc v nghim.Vy phng trnh cho c nghim duy nht: .
Nhn xt : * Ta c dng tng qut ca phng trnh trn l:
(iu kin : ).* Bng my tnh ta c th thy c phng trnh v nghim do ta ngh n chng minh phng trnh vnghim. Thay vo phng trnh th do ta tm cch chng minh VT < VP.
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V d 3: Gii phng trnh :
(THTT).
Gii: iu kin: .
Ta thy phng trnh c mt nghim nn ta phn tch ra tha s .
Ta c:
(Do biu thc trong du () >0).
Vy phng trnh c nghim duy nht .---------------------------------------------------------------------------------------------------------
V d 4: Gii phng trnh: .
Gii: iu kin: .
Nhn thy phng trnh c mt nghim .Phng trnh
Kt hp vi phng trnh ban u ta c :
th li ta thy hai nghim ny u tha mnphng trnh.
Vy phng trnh cho c ba nghim: .
Nhn xt: gii phng trnh ta phi kt hp vi phng trnh ban u. Ta ch rng php bin iny l php bin i h qu do sau khi gii xong ta phi th li cc nghim loi i nhng nghim ngoi lai.Trong cc v d trn ta thy mi phng trnh u c nghim hu t do o vic d on nghim tng i d.Tuy nhin trong nhiu trng hp vic on nghim khng c d dng, c bit l khi tt c cc nghim caphng trnh u l nghim v t! Trong trng hp ny chng ta phi x l th no? Ta xt cc v d sau:
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V d 5: Gii phng trnh :
.
Gii: Do nn .Bng my tnh ta thy c phng trnh khng c nghim hu t, m ch c hai nghim v t. Ta thy
nu th hai v ca phng trnh bng nhau nn ta phn tch ra tha
s .
Ta c:
(do nn khi t lm tha s th biu thc trong du (.) lundng ).
l nghim ca phng trnh cho.Ch : Mu cht ca bi ton l ta c nhn xt , t ta mi nh hng
tm cch phn tch ra tha s . Tuy nhin trong nhiu bi ton th vic tm c nhn t chungkhng cn n gin vy na.
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V d 8: Gii phng trnh: .Gii:
Vi phng trnh ta khng gp c s may mn nh phng trnh trn, bng cch s dng MTBT ta thyphng trnh c hai nghim v t, nu ta linh hot mt cht ta s ngh n tha s chung l mt tam thcbc hai c hai nghim . Vn tam thc y l tam thc no? Cc bn th ngh xem nu bit hainghim ca tam thc th ta c th xc nh c tam thc hay khng? Chc chng ta s tr li l c nh vo
nh l o ca nh l Viet. p dng nh l Viet ta tnh c ( s dng MTBT) . Vy
tha s chng m ta cn phn tch l tam thc nn ta bin i nh sau:
Phng trnh
l nghim ca phng trnh.
Ch : 1) to ra tha s ngoi cch bin i nh trn ta cn c th lm cch khcnh sau:Cch 2: V khng l nghim phng trnh nn.
Phng trnh
=>Phng trnh c hai nghim: .
2) Nu nh chng ta khng c my tnh xc nh c tha s chung l th ta l th no ?.Trc ht ta thm mt lng vo hai v:
8/9/2019 Gii PTVT bng PP lng lin hp
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.
Ta chn m,n sao cho: , t y ta c: .
3) Ta thy c hai cch bin i u lm xut hin tha s chung . Tuy nhin cch th 2 s thun
i hn cch th nht v cch th 2 sau khi t tha s ta ch cn phi gii quyt phng trnh , cn vi cchth nht th ta phi gii quyt biu thc trong du (.) phc tp hn nhiu. Hn na vi cch bin i th haichng ta d sng to ra cc bi ton hn cch th nht.
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V d 9: Gii phng trnh : .
Gii: iu kin : .
Ta thy khng l nghim ca phng trnh nn ta c:
Phng trnh . Bng cch lm nh nu phn nhn xt ta tm
c , do ta thm vo hai v ca phng trnh lng :
Phng trnh
(1).
* Nu
.
Khi (1) ng l mt nghim ca phng trnh.
* Nu
Ta c: (a) c hai nghim v
(b)
.
Vy phng trnh c bn nghim: .Ch : Khi mun thm bt bng cch nhn, chia mt biu thc th ta phi kim tra xem biu thc c
un khc khng hay khng ?---------------------------------------------------------------------------------------------------------
V d 10: Gii phng trnh:
.
8/9/2019 Gii PTVT bng PP lng lin hp
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Gii: k : .
t : (I)Ta thy phng trnh c nghim .Ta bin i nh sau:
(V hai pt: v v
nghim ). .
Kt hp (I) v (II) ta c h :
.
Thay vo phng trnh ban u ta thy ch nghim tha mn.
Vy phng trnh cho c hai nghim v .---------------------------------------------------------------------------------------------------------
V d 11 : Gii bt phng trnh :
.Gii: iu kin :
Bt phng trnh .
.
Kt hp iu kin nghim bt phng trnh : .V d nhin l thm my bi tp cc bn luyn tp
III.Bi tpGii cc phng trnh sau:
1)
2)
3)
4)
5) .
6)
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7) )
8 )
9)
10)
11)
12)
13)