若a,b满足4a²+b²+4a-12b+37=0,求根号a²-2ab的值
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![若a,b满足4a²+b²+4a-12b+37=0,求根号a²-2ab的值](/uploads/image/z/6975086-14-6.jpg?t=%E8%8B%A5a%2Cb%E6%BB%A1%E8%B6%B34a%26%23178%3B%2Bb%26%23178%3B%2B4a-12b%2B37%3D0%2C%E6%B1%82%E6%A0%B9%E5%8F%B7a%26%23178%3B-2ab%E7%9A%84%E5%80%BC)
若a,b满足4a²+b²+4a-12b+37=0,求根号a²-2ab的值
若a,b满足4a²+b²+4a-12b+37=0,求根号a²-2ab的值
若a,b满足4a²+b²+4a-12b+37=0,求根号a²-2ab的值
4a²+b²+4a-12b+37=0
即
(4a²+4a+1)+(b²-12b+36)=0
亦即
(2a+1)²+(b-6)²=0
从而
2a+1=0
b-6=0
故
a=-1/2
b=6
√(a²-2ab)
=√(1/4+6)
=5/2
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