解方程组:(x-1)(y-2)=xy,x(x+2)-4y(y-1)=(x+2y)(x-2y)
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解方程组:(x-1)(y-2)=xy,x(x+2)-4y(y-1)=(x+2y)(x-2y)
{(x-1)(y-2)=xy,(1)
x(x+2)-4y(y-1)=(x+2y)(x-2y) (2)
由(1)
xy-2x-y+2=xy
-2x-y+2=0 (3)
由(2)
x² +2x-4y²+4y=x²-4y²
2x+4y=0 (4)
(3)+(4)
3y+2=0
y=-2/3
代入(4)解得
x=4/3
方程组的解为
{x=4/3
y=-2/3
x(x+2)-4y(y-1)=(x+2y)(x-2y) (2)
由(1)
xy-2x-y+2=xy
-2x-y+2=0 (3)
由(2)
x² +2x-4y²+4y=x²-4y²
2x+4y=0 (4)
(3)+(4)
3y+2=0
y=-2/3
代入(4)解得
x=4/3
方程组的解为
{x=4/3
y=-2/3
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