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

x2+y2
2
−xy的值.

∵x(y-1)-y(x-1)=4,
∴xy-x-xy+y=4,
∴y-x=4,
∴x-y=-4,

x2+y2
2
−xy
=
(x−y)2
2

=
(−4)2
2

=8.