已知集合A={(X,y)|x^2-y^2-y=4},B={(x,y) x^2-xy-2y^2=0}求A∩B这个方程解起来有些困难.

已知集合A={(X,y)|x^2-y^2-y=4},B={(x,y) x^2-xy-2y^2=0}求A∩B这个方程解起来有些困难.
已知集合A={(X,y)|x^2-y^2-y=4},B={(x,y) x^2-xy-2y^2=0}求A∩B
这个方程解起来有些困难.

已知集合A={(X,y)|x^2-y^2-y=4},B={(x,y) x^2-xy-2y^2=0}求A∩B这个方程解起来有些困难.
B={(x,y)| x^2-xy-2y^2=0} = {(x,y)| (x-2y)(x+y)=0} = {(x,y)| x = -y 或 x=2y}
A满足x^2-y^2-y=4：
如果x=-y,那么 (-y)^2-y^2-y=4
y=-4
x=4
如果x=2y,那么 (2y)^2-y^2-y=4
y=-1或4/3
x=-2或8/3
所以A∩B ={ (4,-4),(-2,-1),(8/3,4/3) }

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