已知实数a,b满足a²+b²+a²b²-4ab+1=0,求a+b的值

已知实数a,b满足a²+b²+a²b²-4ab+1=0,求a+b的值
已知实数a,b满足a²+b²+a²b²-4ab+1=0,求a+b的值

已知实数a,b满足a²+b²+a²b²-4ab+1=0,求a+b的值
a²+b²+a²b²-4ab+1=0
a²+b²-2ab+a²b²-2ab+1=0
(a-b)^2+(ab-1)^2=0
a-b=0 ab-1=0
a=b ab=1
a=b=+-1
a+b=2或－2

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