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
(x-y)(xy-1)=56
因为 xy=8
所以 x-y=56/(xy-1)=56÷7=8
x²+y²=(x-y)²+2xy=8²+2×8=80

x²y-Xy²-x+y=56
xy(x-y)-(x-y)=56
(x-y)(xy-1)=56
x-y=56/(xy-1)=56/(8-1)=8
(x-y)^2=x^2+y^2-2xy=64
x^2+y^2=6+2xy=64+2*8=80