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[不等式] 不等式题求证

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等待hxh posted 2014-4-14 15:08 |Read mode
Last edited by hbghlyj 2025-4-12 04:02
  • 已知 $x, y, z \inR^{+}$,求证$$(x y+y z+z x)\left(\frac{1}{(x+y)^2}+\frac{1}{(y+z)^2}+\frac{1}{(z+x)^2}\right) \geq \frac{9}{4}$$
  • 已知非负实数 $a, b, c$ 满足 $a+b+c=1$ ,求证:\[
    2 \leq\left(1-a^2\right)^2+\left(1-b^2\right)^2+\left(1-c^2\right)^2 \leq(1+a)(1+b)(1+c)
    \]

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kuing posted 2014-4-14 15:15
Last edited by hbghlyj 2025-4-12 04:05第一个在人教群里已经有人给了可以阅读的链接了
教师 realnumber 2014-4-14 14:39:32
这里可以阅读的
wenku.baidu.com/view/fdf3586c322b3169a4517723 … f60ddccda38e609.html
伊​朗​9​6​不​等​式​的​2​1​种​证​明

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kuing posted 2014-4-14 15:20

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original poster 等待hxh posted 2014-4-14 15:39
非常感谢,kuing你真神!!

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其妙 posted 2014-4-14 18:34
回复 1# 等待hxh
初学不等式?搞得这么难啊 !

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realnumber posted 2014-4-14 18:54
回复 5# 其妙


    你看他发的题目,没一个简单的.

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isee posted 2014-4-15 00:33
高起点,楼主所发的,偶一个不会

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其妙 posted 2014-4-15 16:42
高起点,楼主所发的,偶一个不会
isee 发表于 2014-4-15 00:33
,一个不会,还有另一个还会,

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其妙 posted 2014-4-15 22:44
kuing不在那个什么AOPS网玩了?

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kuing posted 2014-4-15 23:32
回复 9# 其妙

没以前那劲头了,在自己主场玩算了……

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wanhuihua posted 2018-3-5 20:17

伊朗96有23种证明了,欢迎浏览下载

Last edited by wanhuihua 2018-3-6 21:44伊朗96有23种证明了,欢迎浏览下载
wenku.baidu.com/view/85d0844930b765ce0508763231126edb6f1a76a0

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