x^2+y^2+x^2*y^2+1=4xy
右边是2xy+2xy
移到左边
(x^2-2xy+y^2)+(x^2y^2-2xy+1)=0
(x-y)^2+(xy-1)^2=0
平方相加为0则都等于0
所以x-y=0,xy-1=0
y=x
xy=1即x^2=1
x=±1
所以x=1,y=1或x=-1,y=-1