已知x2-y2=xy,且xy≠0,求代数式x2y-2+x-2y2的值.

问题描述:

已知x2-y2=xy,且xy≠0,求代数式x2y-2+x-2y2的值.

∵x2-y2=xy,
∴原式=

x2
y2
+
y2
x2
=
x4+y4
x2y2

=
(x2y2)2+2x2y2
x2y2

=
3x2y2
x2y2

=3.