TNGHPPHNGTRNH-HPHNGTRNH-BTPHNGTRNHTRONGCCTHITH2014A.HPHNGTRNHCu1. Giihphngtrnh_8x3y3= 63 (1)y2+ 2x2+ 2y x = 9 (2)Hngdn:Ly(1) + 6.(2) (2x 1)3= (y + 2)3.s:(2; 1); (1/2; 4).Cu2. Giihphngtrnh_9y3(3x31) = 125 (1)45x2y + 75x = 6y2(2)Hngdn:Chia(1)choy3,(2)choy2,tu = 3x; v=5y.s:(2/3; 5); (1/3; 5/2).Cu3. Giihphngtrnh_y3+ 3y2+ y 22x + 21 = (2x + 1)2x 1 (1)2x211x + 9 = 2y (2)Hngdn:Ly(1) 2.(2) (y + 1)3+ 2(y + 1) = (2x 1)3+ 22x 1.s:(1; 0); (5; 2).Cu4. Giihphngtrnh_x44x2+ y26y + 9 = 0 (1)x2y + x2+ 2y 22 = 0 (2)Hng dn: t a = x22; b = y3, suy ra (a; b) = {(2; 0); (0; 2)}. s : (2; 3); (2; 3); (2; 5); (2; 5).Cu5. Giihphngtrnh_x36x2y + 9xy24y3= 0 (1)x y +x + y= 2 (2)Hngdn:(1) (x y)2(x 4y) = 0.s:(2; 2); (32 815; 8 215).Cu6. Giihphngtrnh_2_x2+ 3y _y2+ 8x 1 = 0 (1)x(x + 8) + y(y + 3) 13 = 0 (2)Hngdn:ta =_x2+ 3y; b =_y2+ 8x, (a; b) = (2; 3).s:(1; 1); (5; 7).Cu7. Giihphngtrnh___9(x2+ y2) + 2xy +4(x y)2= 13 (1)2x +1x y= 3 (2)Hngdn:ta = x + y; b = x y +1x y (a; b) = {(1; 2); (5/3; 4/5)}.s:(1; 1).Cu8. Giihphngtrnh_(x y)(x2+ xy + y2+ 3) = 3(x2+ y2) + 2 (1)4x + 2 +16 3y= x2+ 8 (2)Hng dn : (1) (x 1)3=(y+1)3y =x 2; (2) 4x + 2+22 3x=x2+8 Linhphailnnh!.s:(2; 0); (1; 3).Cu9. Giihphngtrnh____2x 1 1_2y1=2 22 xx(1)log2 x = y + 2 (2)Hngdn:Rt(2)thayvo(1):2x 1 1 = 1 2 x Bnhphng!.s:(1; 2); 17/9; 2 log2179.Cu10. Giihphngtrnh_x + 3 = 2_(3y x)(y + 1) (1)x2y 1 +x + 12 = 12_6 2y +4 x_(2)Hngdn:(1) _y + 1 3y x_(3y + 1 +3y x)=0.Thayvo(2),dngtnhniu,suyraduynhtnghim.s:(4; 5/2).Cu11. Giihphngtrnh_ln(x + 1) + ln(y + 1) = ln(x 2y + 1) (1)x212xy + 20y2= 0 (2)Hngdn:(2)lphngtrnhngcpthunnht,chiay2.s:(0; 0).Cu12. Giihphngtrnh_xy2+ 4y2+ 8 = x(x + 2) (1)x + y + 3 = 32y 1 (2)Hngdn:(1) (x + 4)(y2x + 2) = 0.Khix = y2+ 2,thayvo(2)y2+ y + 5 = (y2y + 1) + (2y 1) + 5 > (2y 1) + 52_5(2y 1)3_2y 1 Vl.s:(4; 10 + 310).Cu13. Giihphngtrnh____2x + y4x + 2y + 2+_3x + 1x 1= 2 (1)12x + 4y= 5(x 1)(2x + y + 1) (2)Hngdn:(2) 12x + y + 1+1x 1=54,ta =_2x + y4x + 2y + 2; b =_3x + 1x 1.s:(5; 10).Cu14. Giihphngtrnh_x4+ y28x26y= 1 (1)x2y + 2x2+ y= 38 (2)Hngdn:ta = x24; b = y 3.s:(3; 8); (3; 8); (3; 2); (3; 2).www.VNMATH.comCu15. Giihphngtrnh_x3x2y= x2x + y + 1 (1)x39y2+ 6(x 3y) 15 = 336x2+ 2 (2)Hngdn:(1) (x y)(x2+ 1) = x2+ 1,thayvo(2)(x 1)3+ 3(x 1) = (6x2+ 2) + 336x2+ 2 . . . x39x2+ 3x 3 = 0 (x + 1)3= 2(x 1)3.s:_32 + 132 1;232 1_.Cu16. Giihphngtrnh_(4x2+ 1)x + (y 1)1 2y= 0 (1)4x2+ y2+ 4y + 23 4x = 3 (2)Hngdn:(1) (2x)3+2x = (1 2y)3+1 2y, thay vo (1) (2x 1).f(x) = 0. s : (1/2; 0).Cu17. Giihphngtrnh___1 + xy +xy= x (1)1xx+ yy=1x+ 3y (2)Hngdn:Chia(1)chox,ta =1x; b =y.s:(1; 0).Cu18. Giihphngtrnh_x2y2+ 4x2y 3xy2+ x2+ y2= 12xy + 3x 4y + 1 (1)3x22y2= 9x + 8y + 3 (2)Hng dn:(1) (x23x+1)(y2+4y +1) = 2; (2) 3(x23x) 2(y2+4y) = 3. t a = x23x; b =y2+ 4y.s:(3 132; 0); (3 +132; 0); ....Cu19. Giihphngtrnh_10x xy y= 2 (1)30x2xy22xy x y= 1 (2)Hngdn:(1)chiax;(2)chiax2.ta =1x; b = y + 1.s:(1; 4); (1/5; 0); (1/2; 2); (1/3; 1).Cu20. Giihphngtrnh_x4+ x2y2y2= y3+ x2y + x2(1)2y35 2x21 = 0 (2)Hngdn:(1) (x2 y 1)(x2+ y2).Thayx2=y + 1vo(2),xthm,suyranghimduynht.s:(2; 1); (2; 1).Cu21. Giihphngtrnh_(4y 1)(x2+ 1) = 2x2+ 2y + 1 (1)x4+ x2y + y2= 1 (2)Hngdn:Xem(1)lmtphngtrnhbc2theox2+ 1.s:(0; 1).Cu22. Giihphngtrnh_ x + 2 +y 2 = 4 (1)x + 7 +y + 3 = 6 (2)Hngdn:(1) + (2); (1) (2),ta =x + 7 +x + 2; b =y + 3 +y 2.s:(2; 6).Cu23. Giihphngtrnh_2x2(4x + 1) + 2y2(2y + 1) = y + 32 (1)x2+ y2x + y=12(2)Hngdn:(2) _x 12_2+_y +12_2= 1,ta = x 12; b = y +12.Thayvo(1)(1) (4a2+ 11a + 15)(a 1) + 2b2(b 1) = 0 (3)DavoiukinsuyraV T(3)0 a = 1; b = 0.s:(3/2; 1/2).Cu24. Tmmhphngtrnhcmtnghimduynht___x + 3 = 2_(3y x)(y + 1) (1)_3y 2 _x + 52_.m = xy 2y 2 (2)Hngdn:(1) 3(y + 1) (3y x) = 23y x.y + 1 . . . y + 1 3y x = 0.Thayvo(2)(y 2)_2m3y 2 +y + 2 (2y + 1)_= 0s:(; 76/9); 10.Cu25. Giihphngtrnh_ x2+ 21 =y 1 + y2(1)_y2+ 21 =x 1 + x2(2)Hngdn:Ly (1) (2) x2+ 21+x 1+x2=_y2+ 21+y 1+y2, xt hm, suy ra x = y.s:x = 2.Cu26. Giihphngtrnh_ x + y +x y= 4 (1)x2+ y2= 128 (2)Hngdn:Bnhphnghailn(1),rtcy2= 16x 64,thayvo(2).s:(8; 8); (8; 8).Cu27. Giihphngtrnh_xy + x 1 = 3y (1)x2y x = 2y2(2)Hng dn:(1) chia cho y, (2) chia cho y2. t a = x1y; b =xy. s : (12; 12); (2; 1); (1; 1/2).Cu28. Giihphngtrnh_x2+ xy + x + 3 = 0 (1)(x + 1)2+ 3(y + 1) + 2_xy _x2y + 2y_= 0 (2)Hngdn:(1) xy= x2x 3,thayvo(2) 3.yx2+ 2 2_yx2+ 2 1 = 0.s:(1; 3).www.VNMATH.comCu29. Giihphngtrnh_2y32x3= 3 (1)y= 4x3x + 3 (2)Hng dn:Thay (1) vo (2), suy ra y+x = 2x3+2y3(x+y)(x2xy+y212) = 0. T x2xy+y2=12suyray2

23; x2

23. nhgi:|y3 x3||x3| + |y3| 2(_2/3)3 0.s:2/3x2.Cu2. Giibtphngtrnhx3+ (3x24x 4)x + 10 (1).Hngdn:ty=x + 1,chiahaivchoy3,suyraxy.s: 1x(1 +5)/2.Cu3. Giibtphngtrnhx +3 + x3 x< 1 (1).Hngdn:Cunychoimnh!.s:(3; 9).Cu4. Giibtphngtrnh2_1 2x+_2x 8xx (1).Hngdn:(1) 4x 2 + 2x 2x2+ 4x (x22x 2)2 0.s:[2; 0); 1 +5.Cu5. Giibtphngtrnh12 log2(2 + x) + log1/2(4 418 x)0 (1).Hngdn:(1) 2 + x4 418 x,tt =418 x,suyra2t4.s: 2 < x2.www.VNMATH.comCu6. Giibtphngtrnh3_2x2xx2+ 3_< 2(1 x4) (1).Hngdn:tt = xx2+ 3.s: _3 +102< x < 1.Cu7. Giibtphngtrnh2x 3 + 2x + 2342x2+ x 6 (1).Hngdn:Chiahaivchox + 2.s:32x5.Cu8. Giibtphngtrnh6x2(2x + 1 + 1)2> 2x +x 1 + 1 (1).Hngdn: (1) x 32x + 1 + 4>x 1 _2x + 1 32_2>_x 1 +12_2. s: x>10 + 45.Cu9. Giibtphngtrnh2xx +5 4xx

_x +10x 2 (1).Hngdn:tt =x22x + 10.s:x > 0.Cu10. Giibtphngtrnh2x2+ x + 1x + 4+ x24 2x2+ 1(1).Hngdn:(1) 2__x2+ x + 1x + 41_+ x23 2 x2+ 1x2+ 1. . . (x23).f(x)0.s: 3x 3.Cu11. Giibtphngtrnh1 1 4x2x< 3 (1).Hngdn:Linhp!.s:[1/2; 0); (0; 1/2].Cu12. Giibtphngtrnh3 2x2+ 3x + 21 2x2x + 1> 1 (1).Hngdn:1 2x2x + 1 < 0; (1) . . . x2x + 1 < 2x.s:x >13 16.Cu13. Giibtphngtrnh4(x + 1)2< (2x + 10)(1 3 + 2x)2(1).Hngdn:Linhpvphi,(1) 4(x + 1)2