inequality

Mahan73 · New Member Offline Joined: 22 Aug 2009 Posts: 12

It's Iran's second round problem with a little change................
why there isn't any reply? Blush

**Posted:** Sat Nov 07, 2009 7:55 am

dnkywin

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**Posted:** Sat Nov 07, 2009 5:18 pm

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Abdek

Let $a^4 = \frac {x}{y + z + t}$ and $b^4 = \frac {y}{z + t + x}$ and etc..

The inequality may be written as :

$\sum_{sym}\sqrt {\frac {xy}{(y + z + t)(z + t + x)}} \le 2$

Using AM-GM inequality

$\sum_{sym}\sqrt {\frac {xy}{(y + z + t)(z + t + x)}} \le \sum_{sym}\frac {1}{2}\left(\frac {y}{y + z + t} + \frac {x}{x + t +...$

**Posted:** Sun Nov 08, 2009 10:11 am

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