a^2+b^2+a^2b^2=4ab-1
a^2+b^2+a^2b^2-4ab+1=0
(a^2+b^2-2ab)+(a^2b^2-2ab+1)=0
(a-b)^2+(ab-1)^2=0
即
a-b=0
ab-1=0
得
a=b=1或a=b=-1