Question

已知xy=8满足x²y-xy²-x+y=56,求x²+y²的值.

Answer 1

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