(x^2+1)(y^2+1)=4xy
x^2y^2+x^2+y^2+1-4xy=0
(x^2y^2-2xy+1)+(x^2+y^2-2xy)=0
(xy-1)^2+(x-y)^2=0
(xy-1)^2=0,(x-y)^2=0
xy-1=0
x-y=0
解得x=y=1或x=y=-1
当x=y=1时,x^2-3y+1=1-3+1=-1
当x=y=-1时,x^2-3y+1=1+3+1=5
所以x^2-3y+1=-1或5