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](/uploads/image/z/5129025-33-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0a%2Cb%E6%BB%A1%E8%B6%B3a%26%23178%3B%2Bb%26%23178%3B%2Ba%26%23178%3Bb%26%23178%3B-4ab%2B1%3D0%2C%E6%B1%82a%2Bb%E7%9A%84%E5%80%BC)
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