已知xy=8满足x^2y-xy^2-x+y=56,求x^2+y^2的值

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已知xy=8满足x^2y-xy^2-x+y=56,求x^2+y^2的值
已知xy=8满足x^2y-xy^2-x+y=56,求x^2+y^2的值

已知xy=8满足x^2y-xy^2-x+y=56,求x^2+y^2的值
x^2y-xy^2-x+y=56
xy(x-y)-(x-y)=56
(xy-1)(x-y)=56
x-y=8
(x-y)^2=8^2
x^2-2xy+y^2=64
x^2+y^2=64+2xy
=64+16
=80

第一步提取x和y,得x（xy）-y（xy）-x+y=56提取xy得xy（x-y）-（x-y）=56得(x-y)(xy-1)=56所以7(x-y)=56，x-y=8，x^2-2xy+y^2=64

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