已知xy=8且满足x的2次方y-xy的2次方-x+y=56,求x的2次方+y的2次方的值.

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已知xy=8且满足x的2次方y-xy的2次方-x+y=56,求x的2次方+y的2次方的值.

已知xy=8且满足x的2次方y-xy的2次方-x+y=56,求x的2次方+y的2次方的值.
已知xy=8且满足x的2次方y-xy的2次方-x+y=56,求x的2次方+y的2次方的值.

已知xy=8且满足x的2次方y-xy的2次方-x+y=56,求x的2次方+y的2次方的值.
x²y-xy²-x+y
=x²y-xy²-(x-y)
=xy(x-y)-(x-y)
=(xy-1)(x-y)
=56
又∵xy=8
∴(8-1)(x-y)=56,7(x-y)=56
x-y=56/7=8
∴x²+y²
=x²+y²-2xy+2xy
=(x-y)²+2xy
=8²+2×8
=64+16
=80

∵x^2y-xy^2-x+y=56
xy(x-y)-(x-y)=56
(x-y)(xy-1)=56
(x-y)(8-1)=56
∴x-y=8
(x-y)^2=8^2
x^2-2xy+y^2=64
∴x^2+y^2=64+2xy=64+2*8=80

4x³,
∵ xy=8,且x²y-xy²-x+y=56,
∴x²y-xy²-x+y=xy(x-y)-(x-y)=(x-y)(xy-1)=7(x-y)=56,
x-y=8, ∴ (x-y)²=64, x²+y²-2xy=64
∴ x²+y²=64+2*8=80.