设x方y方-20xy+x方+y方+81=0,求x.y的值

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设x方y方-20xy+x方+y方+81=0,求x.y的值
设x方y方-20xy+x方+y方+81=0,求x.y的值

设x方y方-20xy+x方+y方+81=0,求x.y的值
x²y²-20xy+x²+y²+81
=x²y²-18xy+81+x²-2xy+y²
=（xy-9）²+（x-y）²
=0
∴xy-9=0并且x-y=0
∴x=y=3或-3

x^2*y^2-20xy+x^2+y^2+81=0
x^2*y^2-18xy-2xy+x^2+y^2+81=0
(x-y)^2+(xy-9)^2=0
能得到 x-y=0 xy=9
得 x=3 y=3 或 x=-3 y=-3

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