Question

若a²b²+a²+b²=4ab,求a²+b²

Answer 1

a2b2+a2+b2+1-4ab=0

a2b2 -2ab+1 +a2+b2 -2ab=0

(ab-1)2 +(a-b)2=0

==>a=b 且 ab=1

==> a=1,b=1 或 a=-1,b=-1

所以a2+b2=2