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
x²y-xy²-x+y=56
xy(x-y)-(x-y)=56
8(x-y)-(x-y)=56
x-y=56÷(8-1)=8
(x-y)²=64
x²+y²-2xy=64
x²+y²=64+8*2=80