Question

已知xy=8满足x^2y-xy^2-x+y=56,求x^2+y^2的值

Answer 1

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