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[不等式] 四元不等式

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力工 posted 2018-7-13 21:36 |Read mode
已知正数$a,b,c,d$,证明:$(\dfrac{a}{b+c+d})^\dfrac{3}{4}+(\dfrac{b}{c+d+a})^\dfrac{3}{4}+(\dfrac{c}{d+a+b})^\dfrac{3}{4}+(\dfrac{d}{a+b+c})^\dfrac{3}{4}\geqslant 4\cdot 3^\dfrac{-3}{4}$

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kuing posted 2018-7-13 21:45
已知正数$a,b,c,d$,证明:$(\dfrac{a}{b+c+d})^\dfrac{3}{4}+(\dfrac{b}{c+d+a})^\dfrac{3}{4}+(\dfrac{c}{ ...
力工 发表于 2018-7-13 21:36
又一滥用 dfrac 的

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kuing posted 2018-7-13 22:08
很常规的题,过程就不写了,只写一个式子以提示:\[\frac{\sqrt[4]3a}{\sqrt[4]{3a(b+c+d)^3}}\]

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isee posted 2018-7-13 22:15
回复 2# kuing

反正是代码了,,虽然楼主这个指数也用这个,就很难看了,,,,不过,,,,,我自从16:9后反而用dfrac少了

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