若a是1+2b与1-2b的等比中项,则(2ab)/(\a\+2\b\)的最大值我怕看不懂哦.A.(2√5)/15 B.√2/4 c.√5/5 D.√2/2
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![若a是1+2b与1-2b的等比中项,则(2ab)/(\a\+2\b\)的最大值我怕看不懂哦.A.(2√5)/15 B.√2/4 c.√5/5 D.√2/2](/uploads/image/z/10103132-20-2.jpg?t=%E8%8B%A5a%E6%98%AF1%2B2b%E4%B8%8E1-2b%E7%9A%84%E7%AD%89%E6%AF%94%E4%B8%AD%E9%A1%B9%2C%E5%88%99%282ab%29%2F%28%5Ca%5C%2B2%5Cb%5C%29%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E6%88%91%E6%80%95%E7%9C%8B%E4%B8%8D%E6%87%82%E5%93%A6.A.%282%E2%88%9A5%29%2F15+B.%E2%88%9A2%2F4+c.%E2%88%9A5%2F5+D.%E2%88%9A2%2F2)
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若a是1+2b与1-2b的等比中项,则(2ab)/(\a\+2\b\)的最大值我怕看不懂哦.A.(2√5)/15 B.√2/4 c.√5/5 D.√2/2
若a是1+2b与1-2b的等比中项,则(2ab)/(\a\+2\b\)的最大值
我怕看不懂哦.
A.(2√5)/15 B.√2/4 c.√5/5 D.√2/2
若a是1+2b与1-2b的等比中项,则(2ab)/(\a\+2\b\)的最大值我怕看不懂哦.A.(2√5)/15 B.√2/4 c.√5/5 D.√2/2
由等比中项可得:
a^2=(1+2b)(1-2b)
即:a^2+4b^2=1
也即是:|a|^2+(2|b|)^2=1
因为 |a|^2+(2|b|)^2≥4|a||b|
4|a||b|≤1
√|a||b|≤1/2
2ab/(|a|+2|b|)≤2ab/2√(2|a||b|)
≤|a||b|/√(2|a||b|)
=√2/2|a||b|
√(2|a||b|)≤√2/2
2ab/(|a|+2|b|)≤√2/4
开始我看漏了一个条件,换了一种解法,选B