若x(y-1)-y(x-1)=4,求x2+y22−xy的值.
问题描述:
若x(y-1)-y(x-1)=4,求
−xy的值.
x2+y2
2
答
∵x(y-1)-y(x-1)=4,
∴xy-x-xy+y=4,
∴y-x=4,
∴x-y=-4,
∴
−xy
x2+y2
2
=
(x−y)2
2
=
(−4)2
2
=8.