X^2+Y^2+X^2Y^2-4XY+1=0,求(X-Y)^2008-(XY)^2008的值
问题描述：
X^2+Y^2+X^2Y^2-4XY+1=0,求(X-Y)^2008-(XY)^2008的值
答
(X-Y)^2+(XY-1)^2=0
X-Y=0,
XY=1.
(X-Y)^2008-(XY)^2008=-1.
答
X^2+Y^2+X^2Y^2-4XY+1=0
(X^2+Y^2-2XY)+(X^2Y^2-2XY+1)=0
(X-Y)^2+(XY-1)^2=0
上式成立必须有：x-y=0
xy-1=0,xy=1
(X-Y)^2008-(XY)^2008
=0^2008-1^2008
=0-1
=-1