. x^, 4x +3 y, Ta thay phuong trinh c6 nghỉm khi va chi khi — va
Khidota thu dug-c h§ phuong trinh: ab =
ab = 2
, 3 + i b 3= 3 a 2+ | b- 5 '
ab = 2 ^y,,
2â+b^=6â+3b-10 ^ 2 ' 2 ^ 2 ' 2 ^
Tir h? phuong trinh ban dau ta nham dugc nghỉm la x = y = 1 nen ta se c6 h# nay c6 nghỉm khi: a = 2; b = 1 h# nay c6 nghỉm khi: a = 2; b = 1
[(a-2)b = 2 ( l - b )
Dod6tasephantichheved,ng:|^^_^^,^^^^^^^^_^^,^^^^^^ ^ 2 ( l - b ) ^ 2 ( l - b ) Vi ta luon c6: b ^ 0 nen tu phuong trinh tren ta rut ra a - 2 = — - — The xuong phuong tririh duoi ta dugc:
i ^ ^ ^ ( a +1) = (b - l)Hh + 2) o (b - if [4(a +1) - b2(b + 2)] = 0 b = l b = l
i ^ ^ ^ ( a +1) = (b - l)Hh + 2) o (b - if [4(a +1) - b2(b + 2)] = 0 b = l b = l • The len phuong trinh tren taco:
b + 2
i ( ^ = b ^ ( b . 2 ) . b b
b = -2 => a = -1 o X = -2; y = - -
b^ = 4 (Khong TM) V^y h? da cho c6 2 nghi^m la: (x;y) = (1;1), V^y h? da cho c6 2 nghi^m la: (x;y) = (1;1),
x > - l d) Dieu ki^n: d) Dieu ki^n:
y >0 . Ta Viet lai h? phuong trinh thanh:
^ 2 ( x - y ) 2 + 6 x - 2 y + 4 - ^ = Vx+T
<=> ^ 2 ( x - y ) ^ + 6 x - 2 y + 4 = ^y + Vx + 1 . Binh phuong 2 ve ta thu dugc: 2x^ - 4xy + 2y^ + 6x - 2y + 4 = x + y +1 + 2^y(x +1)
o2l{x + lf -2y(x + l ) + y 2 l + (x + l + y) = 27y(x + l )
<:i>2(x + l - y) 2+ ( V^ - V y) ^ = 0 « | ' ' / ^ ^ ^ < » x + l = y [ Vx +1 = ^ y [ Vx +1 = ^ y
Thay vao phuong trinh (2) ta c6:
Dlt a = ^ y ( y - 7 ) ta c6 phuong trinh: , :! a ^ - 1 a ^ - 1 Vâ +1 = a +1 < o a^ - a 2- 2 a = 0 a>-l a = 0 a = - l a = 2 Voi a = 0: y = 0=>x = - l y = 7=>x = 6 Vol a = - l= > y 2 - 7 y + l = 0<:> 7-3S 5-3S y = =>x = — ^ 2 2 7 + 375 5 + 3>/5 y = — - — = > x = ^ Voi a = 2 r: > y 2 - 7 y- 8 = 0 0 y = - l (L) y = 8=>x = 7 H | phuong trinh da cho c6 nghỉm la :
(x;y) = (-l;0),(6;7). 5-3N/5 7 - 3 V 5 ' 5 + 375 7 + 375
,(7; 8) Vi 2: Giai cac phuong trinh sau Vi 2: Giai cac phuong trinh sau
,2
a)
c)
x ^ - ( 2 y + 2 ) x- 3 y 2= 0
x^ + 2xy2 - (y + 3)x - 2y^ - 6y2 +1 = 0 x^ + x y + 9y = y^x + y^x^ + 9x x^ + x y + 9y = y^x + y^x^ + 9x
x(y3-x^) = 7 d)
x^ -2xy + 2y^ +2y = 0 x^ - x 2 y + 2 y 2 + 2 y - 2 x = 0 x^ - x 2 y + 2 y 2 + 2 y - 2 x = 0
xy^ - 3x^y - 4yx^ - y + 3x^ = 0
3 x^ y- y 2 + 3 x y + l = 0
G i i i :
a) Cach 1: Lay phuong trinh thu hai tru phuong trinh thu nhat theo ve ta du(?c: 2xy^ - (y + 3)x - 2y^ - 6y^ +1 + (2y + 2)x + 3y2 = 0 du(?c: 2xy^ - (y + 3)x - 2y^ - 6y^ +1 + (2y + 2)x + 3y2 = 0
O 2xy2 + xy - 2y3 - 3y^ +1 - X = 0 < » X (2y^ + y _ 1J _ 2y3 - 3y^ +1 = 0
« ( y + l ) ( 2 y - l ) ( x - y - l ) = 0.
+ Neu y = -1 thay vao phuong trinh (1) ta c6: x^ = 3 o x = ±73