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[不等式] 除了全相等还能咋取等(

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hbghlyj posted 2021-4-7 15:06 |Read mode
Last edited by hbghlyj 2021-4-8 00:53整数$n\ge2$,正实数$a_{1}, a_{2}, \cdots, a_{n}, x_{1}, x_{2}, \cdots, x_{n}$,满足$\sum_{1 \leq i<j \leq n} x_{i} x_{j}=n$,证明$\sum_{i=1}^{n}\left(\frac{a_i}{\sum\limits_{j \neq i} a_{j}} \cdot \sum\limits_{j \neq i} x_{j}\right) \geq n$
据说取等不唯一

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kuing posted 2021-4-7 15:26
条件那里是 =1 还是 =n?

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original poster hbghlyj posted 2021-4-8 00:55
Last edited by hbghlyj 2021-4-8 01:02回复 2# kuing
应该是我打错了. 已经改正了

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