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利用常见不等式推导“对数均值不等式”

2023-06-22 14:36 作者:数学老顽童  | 我要投稿

我们熟知:

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在上式中,换元,令x%3D%5Cfrac%7Ba%7D%7Bb%7D

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%5Cln%20%20a-%5Cln%20%20b%3E%5Cfrac%7B2%5Cleft(%20a-b%20%5Cright)%7D%7Ba%2Bb%7D

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我们熟知:

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在上式中,换元,令x%3D%5Cfrac%7Ba%7D%7Bb%7D

%5Cln%20%5Ccolor%7Bred%7D%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%3C%5Csqrt%7B%5Ccolor%7Bred%7D%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%7D-%5Cfrac%7B1%7D%7B%5Csqrt%7B%5Ccolor%7Bred%7D%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%7D%7D

%5Cln%20%20a-%5Cln%20%20b%3C%5Cfrac%7Ba-b%7D%7B%5Csqrt%7Bab%7D%7D

%5Cfrac%7Ba-b%7D%7B%5Cln%20%20a-%5Cln%20%20b%7D%3E%5Csqrt%7Bab%7D.

综上所述:

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利用常见不等式推导“对数均值不等式”的评论 (共 条)

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