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