已知实数a与b满足a+b=1,求代数式1/a+2/b的最小值
p.s:1/a+2/b为什么等于3+b/a+2a/b?
人气:481 ℃ 时间:2019-09-16 21:21:47
解答
1/a+2/b
=(1/a+2/b)(a+b)(a+b=1)
=1+b/a+2a/b+2
=3+b/a+2a/b
>=3+2根号2
当b/a=2a/b取等,
最小值是3+2根号2.
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一般有两个数是1的,你要注意替换了!
这一题目是经典的题目了,好好看一看了!
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