已知xy=8满足x²y-xy²-x+y=56,求x²+y²的值.

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已知xy=8满足x²y-xy²-x+y=56,求x²+y²的值.

已知xy=8满足x²y-xy²-x+y=56,求x²+y²的值.
已知xy=8满足x²y-xy²-x+y=56,求x²+y²的值.

已知xy=8满足x²y-xy²-x+y=56,求x²+y²的值.
x²y-xy²-x+y=56
xy(x-y)-(x-y)=56
(xy-1)(x-y)=56
xy=8;所以(x-y)=8
(x-y)^2=64
X^2-2xy+y^2=64
x^2-16+y^2=64
x²+y²=64+16=80