Chuyen de phuong trinh he phuong trinh on thi dai hoc

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Chuyen de phuong trinh he phuong trinh on thi dai hoc

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  • 1. Chuyn Phng trnh, bt phng trnh, H phng trnh . .d x a x b x c mx d a b c m d a d b d c . t y x d .t x a b mx nx pbx d cx dmx c px cnx c qx cmx c pxnx c qx c x x x x x xx x xx x x xx x x xx x x xGV: NGUYN MNH HNG TEL: 09478766891CHUYN : PHNG TRNH, BT PHNG TRNH , H PHNG TRNHA. PHNG TRNH .I. MT S PHNG TRNH I S BC CAO.1. Phng trnh dng: ax4 bx3 cx2 bx a 0 (Phng trnh ny gi l phng trnh i xng bc 4). gii phng trnh ny ta chia c hai v cho x2 (x 0) . Ri t n ph t x 1x2. Phng trnh dng ax4 bx3 cx2 kbx ka2 0, k . (Phng trnh ny gi l phng trnh hi quy). gii phng trnh ny ta cng chia cho x2 v t n ph t x kx3. Phng trnh dng (x a)(x b)(x c)(x d) m, a d b c , Ta nhm(x a)(x d)(x b)(x c) m , t i n cch t n ph.4. Phng trnh dng (x a)(x b)(x c)(x d) mx2 , ad bc . Ta nhm(x a)(x d)(x b)(x c) mx2 , ri chia hai v cho x2 v t n ph t x adx 5. Phng trnh dng ( )( )( ) , , ( )( )( )26. Phng trnh dng (x a)4 (x b)4 c , t n ph2 7. Phng trnh dng2 22 22 222 200ax axax axax axaxax ax Bi 1: Gii cc phng trnh.a. (x 1)4 2(x4 1) b. x4 10x3 26x2 10x 1 0 c. x4 3x3 3x 1 0d. x4 3x3 14x2 6x 4 0 e. x4 9 5x(x2 3) f. (x2 6x 9)2 x(x2 4x 9)Bi 2. Gii cc phng trnh.a. x(x 1)(x 1)(x 2) 3 b. (x 2)(x 3)(x 7)(x 8) 144 c. (x 5)(x 6)(x 8)(x 9) 40d. (6x 5)2 (3x 2)(x 1) 35 e. 3(x 5)(x 6)(x 7) 8x f. x4 2x2 8x 3g. (x 2)4 (x 8)4 272 h. x4 24x 32 i. x4 8x 7Bi 3. Gii cc phng trnha. 2 7 12 23 2 3 5 2b.22 210 15 4 06 15 12 15 c.2 22 23 5 5 5 14 5 6 5 4

2. Chuyn Phng trnh, bt phng trnh, H phng trnh4 12( 2) x x xx x x20 2 5 2 48 4 0 x x xg x f x g x f x f x f x g x h x g x g x f x g x f x g x h x f x g x k xf gxac nhx x x x xxGV: NGUYN MNH HNG TEL: 09478766892d.222x xxe.2 2 221 1 1f.222 15( 1)II. PHNG TRNH V TCc phng trnh c bn.2( ) 0( ) ( )( ) ( )f x g xf x g x ( ) 0, ( ( ) 0)( ) ( )( ) ( )f x g xf x g x( ) 0 ( ) 0( ) ( ) ( ) ( ) 0 ( ) 0( ) ( ) 2 ( ). ( ) ( ) 2 ( ). ( ) ( )33,( ) ( )( ) ( ). f x g xf x g x+) Phng trnh 3 A 3 B 3 C A B 33 AB(3 A 3 B) C sau th 3 A 3 B 3 C a phng trnh vdng A B 33 A.B.C C+) Nu phng trnh c dng c dng f (x) h(x) g(x) k(x) c f (x) g(x) k(x) h(x) th chuynphng trnh v dng: f (x) g(x) k(x) h(x) , Bnh phng v gii theo phng trnh h qu.+) Nu phng trnh c dng f (x) h(x) g(x) k(x) vi f (x).g(x) k(x).h(x) , ta chuyn phng trnhv dng f (x) g(x) k(x) h(x) ri bnh phng hai v v gii phng trnh h qu.Dng 1: Phng php bin i tng ngBi 4. Gii cc phng trnha. x2 3x 10 x 2 b. 2x 1 1 x(3 x) c. x 3 2x 8+ 7 xd. x x 8 1 x 1 e. x(x 1) x(x 2) 2 x2 f. 4 3 10 3x x 2Bi 5. Gii cc Phng trnha. 5x 1 x 1 2x 4 b. 3x 3 5 x 2x 4 c. 10x 1 3x 5 9x 4 + 2x 2d. x 3 3x 1 2 x 2x 2 e.31 1 2 1 22Bi 6. Gii phng trnha. 3 x 2 3 2x 3 1 b. 3 2x 3 3 x 312(x 1) c. 2x 1 x2 3x 1 0Dng 2: Phng php t n ph1. Phng trnh dng 1: a. f (x) b f (x) c 0 . t t f (x),t 0.2. Phng trnh dng 2. a f (x) m b. f (x) n c f (x) p , t t f (x) 3. Chuyn Phng trnh, bt phng trnh, H phng trnha x x x x x x x c x x x x x x x a x x x x x c x x x x xa x x x x x GV: NGUYN MNH HNG TEL: 094787668933. Phng trnh c f (x) g(x) v f (x).g(x) , nhng f (x) g(x) k : const ta s tt f (x) g(x) suy ra f (x).g(x) theo t. v a phng trnh cho v n t, gii ra v tm ra t.4. Phng trnh c cha f (x); g(x) trong f (x). g(x) k ta t n ph t f (x)5. Phng trnh c dng a.A(x) b.B(x) c. A(x).B(x) , ta xt hai trng hp ca B(x)=0 v B(x) 0,vi B(x) 0 ta chia hai v phng trnh cho B(x).6. Phng trnh c dng au bv c mu2 nv2 , bnh phng hai v ca phng trnh a phngtrnh v phng trnh ng cp bc hai.Bi 7. Gii cc phng trnh2 2 2 .( 4)( 1) 3 5 2 6 b. 2(x 3 1) 3 3 022 2 2 25 3 . 3 4 5 4 1 0 d. 2 3 114 2e. x 17 x2 9 x 17 x2 f. x 5 x 1 6 (HD: t t x 1,t 0. Ta c nghim l11 172x ) g. x (2014 x )(1 1 x )2 (HD: t t 1 x -> x=0)Bi 8. Gii phng trnh3 2 49 13 . 3 1 8 24 1 b. 5 ( 1)( 4) . 3 2 1 2 3 22 4 2 d. 3 x+ 6 x= (x 3)(6 x)+3 e. 2x 3 x 1 3x 2 2x2 5x 3 2f . x 1 4 x (x 1)(4 x) 5 g. 3 2 x 6 2 x 4 4 x2 10 3x (B-2011)Bi 9. Gii phng trnh. 2(x2 3 2) 3 3 8 b. 3 1=x2+3x-1 c. x2-3x+1= - 3 4 2 13d. x 2 x 6 3 x 1 3 x 2 6 x19e. 2(x2 2) 5 x3 1 f. 2x2 5x 1 7 x3 1 g. x3 3x2 2 (x 2)3 6x 0h. x2 3 x2 1 x4 x2 1 i. x2 2x 2x 1 3x2 4x 1k. 5x2 14x 9 x2 x 20 5 x 1Dng 3.t n ph nhng vn cn n ban u (cn gi l t n ph khng hon ton)Bi 10. Gii cc phng trnh 4. Chuyn Phng trnh, bt phng trnh, H phng trnh x x x x GV: NGUYN MNH HNG TEL: 09478766894a. 2(1-x) x 2 2 x 1 = x2-2x-1 b. 2( 2( x 2)+2 2 x ) = 9 x 2 16 c. x2+3x+1= (x+3) x2 12 2 x2- 2 1 1 xd. (4x-1) x 1 2 x 2 x 1 e . 3x - (x+1) x 4 x 5 + 5=0 f. 1 +3 x = 2x + 1x x xg. 4 1 x 1 3x 2 1 x 1 x2Dng 4. a v phng trnh tchPhng trnh c dng: u+v=1+uv(u 1)(v 1) 0Phng trnh c dng: au bv ab uv(u b)(v a) 0Bi 11. Gii cc phng trnh saua. x 2 7 x 10 3 x 2 2 x 5 6 b. 2 x 2 3 x 2 3 x 5 3 x 2 2 x 2 9 x5c. x +3 8 x 3 x 2 x 2 10 x 16 2 d. x - 4 x 4 ( x 4) x 2 x ( x4) 0Bi 12. Gii phng trnha. x 2 x 1 ( x 1) x x2 x =0 b. x +2 7 x =2 x 1+ x2 8 x 7 +1Bi 13. Gii cc phng trnha. x 1 2( x 1) x 1 1 x 3 1 x2 b. x 1 x3 x2 x 1 1 x4 1c. 3 x x 3 x d. 2 x 3 9x2 x 4e. 2 3.3 9x2 (x 2) 2x 33 3x(x 2)2Hng dn : c. Bnh phng hai v ta c phng trnh 3 3 3 0 ( 1 )3 103 3 3d. HD: Phng trnh tng ng (1 3 x)2 9x2e. Phng trnh tng ng 33 x 2 3 3x 0 -> x=1Dng 5. a v ptr cha du GTT v gin c cc tha s ging nhau c 2 v.I.a v phng trnh cha du GTTBi 14. Gii cc phng trnh sau 5. Chuyn Phng trnh, bt phng trnh, H phng trnhx x x x x x x x xa. 3 4 1 3 4 1 4 b. 2 1 2 1 3x x x x x x x xx x x x x xa. x(x 1) x(x 2) x b. x 3x 2 x 4x 3 2 x 5x 4c. x 2009x 2008 x 2010x 2009 2 x 2011x 2010d. x(x 1) x(x 2) 2 x(x 3)a . x 3x 2 x x 1 4 x 3 b. (2 x ) (2 x )7 x ) (7 x ) 3c. x ( x 1 1)( x 17 5) d. x 2 4 x 2 x 5 2 x 5 x c. x 3x 2 x 3 x 2 x 2x 3 d. 2 x 7x 10 x 12x 20 xe. 3x 7x 3 x 2 3x 5x 1 x 3x 4 f. 3x 1 6 x 3x 14x 8 0(B.2010) u a f xv b f x GV: NGUYN MNH HNG TEL: 0947876689522 2 2 1 2 1 2 2 c. 6 9 2 2 1 d. 1 22e. 2 2 1 10 6 1 2 5 4 1 II.Phng php gin cBi 15. Gii cc phng trnh2 2 2 22 2 2Dng 6. Phng php nhn lin hpBi 16. Gii cc phng trnh sau2 2 3 2 3 3 22 Bi 17. Gii cc phng trnha. 2 x 2 x 6 x 2 x 3 2(x 3 ) b.1 x 2x 2 4x 2 1 2x 1x2 2 2 22 2 2 2 2g. x2 15 3x 2 x2 8 h. 2x2 16x 18 x2 1 2x 4i. 2x2 11x 21 33 4x 4 0 k. 3 x2 1 3x3 2 3x 2l. 3 x2 4 x 1 2x 3 m. 2x2 x 1 x2 x 1 3xDng 7. Phng php a v h+) n a f (x) m b f (x) c . a v h bng cch t: ( )( )nm+) Phng trnh c dng: x2 x a a . a v h bng cch t: t x 5 , Ta c h:2255x tt x+) Phng trnh c dng: n ax b c(dx e) mx n, vi d ca m;e cb n , a v h bng cch: tn ax b dy e 6. Chuyn Phng trnh, bt phng trnh, H phng trnha. x 3 10 x 5 b. x 7 x 1 c. 8 x 8 x 1 d. 17 x 2x 1 12 1 1 x x k. x 5 x 1 6x xx x a. x x 7 7 b. x +1=2 2x 1 c. x x 5 5 d. 4 4 x xe. 2(x 1) x 3 2 f. 2x 15=4(8x +8x 5)x x x x x x x f. x3 3x x 2 (trch t THTT).x x x x x xa. 1+ 1 x 2 x b. x + (1 x ) =x 2(1 x )(1 x )c. 2 x 1 x = d. 64x 112x +56x 7 2 1 xGV: NGUYN MNH HNG TEL: 09478766896Bi 18. Gii cc phng trnh sau2 2 3 3 3 4 2 3 24 4 3 2 3 2 3 2 3e. 41 x 41 x 4 f. (3x 1) (3x 1) 9x 1 1 g.2 3x 2 3 6 5x 8 0(A.09)h. x 3 25 x3 x 3 25 x3 30 i. 442l. 6 2 6 2 85 5 3Bi 19. Gii cc phng trnh4 2 4 3 4 3 4 2 3 2 3 2 2a. x x(1 x) (1 x) 1 x x x (1 x) b.5 x 1 2(x 2) c. 10 x 8 3(x x 6) e. x(x 2) 2x 1 3x 4x 1Bi 20. Gii cc phng trnh2 3 3 22 22g. 4 9 7 2 728 h. x2 6x 3 x 3 i. 3 3x 5 8x3 36x2 53x 25k. 3 12x 7 64x3 96x2 40x 3 l. 53 2x 1 81x3 162x2 117x 17Dng 8. Phng php lng gic haBi 21. Gii cc phng trnha. 1 1 x2 x(1 2 1 x2 ). b. 1 1 x2 (1 x)3 (1 x)3 2 1 x2c. x 2x 1 d. 3x 1 x2 4x31 x2e.21 1 2 (1 )3 (1 )3 2 13 3g.2 2 2221 1 ( 1)2 2 (1 )h. 3 1 6x 2xBi 22. Gii cc phng trnh2 2 3 2 3 22 32 6 4 2 221 x 7. Chuyn Phng trnh, bt phng trnh, H phng trnhDng 9. Phng php hm sNi dung phng php:*Nu phng trnh c dng: f (x) m . Xt hm s y f (x) , nu hm s ny lun ng bin hoc nghchbin trn khong I (min I l cc khong, on khng ri nhau) nu phng trnh c nghim x0 th phngtrnh c nghim duy nht.* Nu phng trnh c dng f (x) g(x) . Dng lp lun (thng l dng o hm) khng nh hm f(x),g(x) theo th t ng bin, nghch bin trn mt khong I (v ngc li).Tm ra nghim x0 ca phng trnh phng trnh trn, th th phng trnh c nghim l duy nht.* Nu phng trnh c dng f (x) f ( y) , vi hm s c trng y f (t) lun ng bin hoc nghch bintrn min I th th trn I phng trnh f (x) f ( y) tng ng vi x=y.* Nu phng trnh c dng f (x) m . Trong hm f(x)=0 c mt nghim trn min I th th phngtrnh f (x) m c nhiu nht hai nghim trn I.Bi 23. Gii cc phng trnha. 9x 1 9x2 1 2 b. x2 35 x2 24 5x 4c. (2x 5)3 21 6x 3 2x 5 (7 2x)3 0 d. 2 1 2 1 2 2 02 1 1 x x x x| | 8 6 1 | 3 1|x xx x xsin 16cos 2cosx x xx x2 (2 ) 4x . i. 4 x2 1 x 1 k. 4x 1 4x2 1 1x xx x GV: NGUYN MNH HNG TEL: 094787668972x xx x e. 1 1 2x 1 8x 15f. 22| 3 | g.6 4254 51cosxh.2222 tan1 vi (0; )2l. x5 x3 13x 4 0 m. 3x 2 3 9x2 (4x 2)1 1 x x2 0n. x3 4x2 5x 6 3 7x2 9x 4 o. 1 4 510 12p. x (1 x)3 1q. x 1 3x x2 x 1 r. 3 x 6 x2 7 x 1s. (x 1)3 (5x x2 )3 3 5x x2 3(x 1) t. 3 x 2 8x3 60x2 151x 128 .x x x 5u. 1 1 v. x7 x5 18x 5 0w. x2 (3x4 2) (24x 21) 8x 7 2 8x 7 8Dng 10. Mt s phng php khc.Bi 24. Gii cc phng trnh (a v tng cc s ko m)a. 4 x 1 x2 5x 6 b. x y 1+2y x 1= 3 xy2c. x4 -2x2 x 2 2x 16 +2(x2 -3x+10)=0 d. x + y-1 + z 2 1 (x y z).2 Bi 25. Gii cc phng trnh (nh gi) 8. Chuyn Phng trnh, bt phng trnh, H phng trnhg. 5x 3x 3x 2 x 3x 1 . h. x 2x 2x 1 3x 4x 1b. 4 x 2 2x 1 2 c. x 16 x 3 7x 2x x 3 x 3d. 2 1 3 e. x 5 x 4 7 x 2x x x x x x x x 2 x 3 x 2 x 3 a. x 4m 16 2 x 2m 4 x 0 b. x x m x mGV: NGUYN MNH HNG TEL: 09478766898a. x 7 9 x x 2 16x 66 b. x 9x 1 29x 1 xc. x2 3x 9 (x 2 2x 2)(x 2 4x 7) d. x 2 4x 6 2x 2 5x 3 3x 2 9x 5 2e. 5 2 7 4x 3 2 1. f . 7x 2 22x 28 7x 2 8x 13 31x 2 14x 4 3 3(x 2).x 1 23 2 2 22222 2x 6x i. 15 x 6x 18x 6x 11Bi 26. Gii cc phng trnha . ( x 1 1) 3 2 x 1 2 x22 2 Bi 27. Gii cc phng trnh sau.a. x2 2x 5 x2 2x 10 29 b. 3 x 1 7x (x2 9)(x 48)2 2 x2 c. x (x 2) x (4 x) 33d. 2(x 1)2 1 2(x 3 1)2 2 3 2(x 3 1)2 2 3 32 2 4 4 4 4Dng 10. Bi ton cha tham sBi 28. Gii v bin lun cc phng trnh sau.222(x 1) x 1Bi 29.Tm m phng trnh sau c nghim duy nht.4 x x 5 m b. 4 x2 2x 4 x 1 mBi 30. Tm m phng trnh sau c nghima. x 3 6 x (x 3)(6 x) m b. x2 3x 2 x2 3mx 3mc. m( 1 x2 1 x2 2) 2 1 x4 1 x2 1 x2 (B- 2004) d. 3 x 1 m x 1 24 x2 1 (A-07)Bi 31. Tm m phng trnh sau c ng hai nghim thc phn bit.a. x2 mx 2 2x 1 (B- 2006) b. x2 2x 8 m(x 2) (B-2007)c. 4 2x 2x 24 6 x 2 6 x m (A -2008)III. PHNG TRNH M, LGARIT. 9. Chuyn Phng trnh, bt phng trnh, H phng trnhlog (4 4).log (4 1) log 1x x b. 4 2 2 4 log (log ) log (log ) 2 x x c. 225 log (125 ).log 1 x x x log 3 log log 3 log 1x x 2 x x e. (x 2)log3 9( x2) 9(x 2)31 log ( 3) 1 log ( 1) log (4 )2 43 log 1 ( 2) 3 log (4 ) log ( 6)2 4x x x e. 2 3 3x x x x x x d.log 5 log 5 x6.5 x 11 x x x x x x h. log6 e. Chia hai v cho x2, s: 3; 1; 3 21GV: NGUYN MNH HNG TEL: 09478766899Bi 32. Gii cc phng trnh (t n ph)a. 4x x2 2 5.2x1 x2 26 6 0 b. 32x1 3x2 1 6.3x 32( x1) c. 432cos x 7.41cos x 2 0d. 5.2x 7 10x 2.5x e. (26 15 3)x 2(7 4 3)x 2(2 3)x 1Bi 33. Gii cc phng trnh sau:a. 12 2 128d. 3 3f. 2 2 2 2 2 log (1 ) ( 5) log( 1) 5 0 x x x x g. 222 log x 1 log x 1Bi 34. Gii cc phng trnh (a v phng trnh tch)a. 52x1 7x1 175x 35 0 b. x2.2x1 2|x3|6 x2.2|x3|4 2x1 c. 4x2 x 21x2 2( x1)2 1d. 82 4 21 14 4f. 2 3 4 20 log x log x log x log x g. 2 2 23 3 6 log (x x 1).log (x x 1) log (x x 1)Bi 35. Gii cc phng trnh (Lgarit ha)a.4 1 3 2 2 15 7b. xlog x 1000x2 c.log 53 105 logx x1511Bi 36. Gii cc phng trnh (Phng php hm s)xa. 6x 8x 10x b. 2 1 32x c. 2 3x x2 8x 14 d. 3.25x2 (3x 10)5x2 3 x 0e. x2.3x 3x (12 7x ) x3 8x2 19x 12 f. x2.3x1 x(3x 2x ) 2(2x 3x1)g. 5 4 3 2 1 1 1 2 3 5 2 7 17.2 3 6x x x x2 6 log (x 3 x ) log xi. 2 3 log (1 x ) log x k. xlog2 9 x2.3log2 x xlog2 3 l. 2 3 4(x 2) log (x 3) log (x 2) 15(x 1)HNG DN V P SBi 1.a. Khai trin v rt gn c phng trnh x4 4x3 6x2 4x 1 0 x 1 3 3 2 3b. Phng trnh i xng, s: x 3 8, x 2 3 c. Phng trnh hi quy, s: 1 2; 1 52x x d. Phng trnh hi quy, 1 3; 5 332x x 2x f. Chia hai v cho x2, s: 9; 1; 5 612 .Bi 2. 10. Chuyn Phng trnh, bt phng trnh, H phng trnh c. x 10;4 d. 5 21x xx x f. 3 21 ; 5 5x x f. x 3.u x x u u l ri tm ra x.u u l x b. x 5; x 8 c. 2; 5t x x t t x Bi 9. a. x 3 13 b. v nghim c. x 1Bi 10. a.t u x2 2x 1u2 x2 2x 1 x2 2x 1 u2 4x , ta c phng trnh :u2 2(1 x)u 4x 0u 2 u 2x x 1 6 .b. t k v bnh phng hai v, ta c phng trnh 4(2x 4 8 4x 4 2(4 x2 )) 9x2 16 . a phngtrnh v dng: 4(8 2x2 ) 16 8 2x2 x2 8x 0 . t u 8 2x2 x 4 2. x e. 2; 5 1 5 u xu x u x u x x x x GV: NGUYN MNH HNG TEL: 094787668910a. 1 132x b. 6; 1; 5 1532x6e. t y = x+9, x 9f. 1 2 g. 4;6 h. 1 5 i. 1 2 8 2 2 2 .Bi 3.a. Chia c t v mu cho x, ta c 11 976x b. x 3;5;9 66 c. 4 11d. Thm 2 . 22vo c hai v v c x 1 5 e. 3; 232 2Bi 4. a. x 14 b. x 1;2 2 c. x 5; x 6 d. x 8 e. 0; 98Bi 5, Bi 6: tng t bi 4.Bi 7. p s: a. x 2; x 7 b. t 2 3 2 1 ( )2c. t u x2 4x 5 u 1 u 4(l) x 2 d. x 1; x 2Bi 8. a. t u 4 x 1 suy ra 2 4 ( ) 1533x x d. t u 3 x 6 x u 3 u 1(l) x 3; x 6e. t u 2x 3 x 1u 3 u 2(l) x 25 6 17 f. x 0; x 3g. Bin i phng trnh v dng: 3( 2 x 2 2 x) 4 4 x2 10 3x , t2 2 2 0, 3 653c. x 2 2 d. t u x2 1 434x x f. t u 1 1 u2 (1 3 x 1)u 2x 0 u 2( 1 x 1) u 1 x 1x2x g. t 2 2 1 3 1 (2 1 ) 2(1 2 1 ) 0 0,2 1 5u x .Bi 11. a. x 2; x 4 b. x 5 c. x 5 d. x 8 11. Chuyn Phng trnh, bt phng trnh, H phng trnhGV: NGUYN MNH HNG TEL: 094787668911Bi 12. a. x 2 b. x 4; x 5Bi 13. a. t iu kin v bin i phng trnh v: ( 1 1 )(2 1 1 1) 0 0; 2425x x x x x x b. x=2.____________________________________________________________________________________________ 12. Chuyn Phng trnh, bt phng trnh, H phng trnh8x a. 6x 1 4x 1 0 c. x 4x 5+2x 3 b. x 2x 15 x 2 d. 4 1 x - 2 x > 0x 2 x e.x x > 35 f. 0 g. x 1 x 1 2 h.1 3 1 1 a. x 3 2x 8+ 7 x b. (x - 4x) 2x 3x 2 0 c. 2x