Titu Andreescu

by v_Enhance, Jul 11, 2011, 12:32 AM

(MOP 1999, Titu Andreescu) Prove that for positive real numbers $a$, $b$, $c$,

\[ \frac{1}{a+b} + \frac{1}{b+c} + \frac{1}{c+a} + \frac{1}{2\sqrt[3]{abc}} \geq \frac{(a+b+c+\sqrt[3]{abc})^2}{(a+b)(b+c)(c+a)} \]



Making sure we know how to expand? -____-"
This post has been edited 1 time. Last edited by v_Enhance, Jul 11, 2011, 12:32 AM

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Anyways, Solution
This post has been edited 2 times. Last edited by v_Enhance, Jul 11, 2011, 12:38 AM

by v_Enhance, Jul 11, 2011, 12:37 AM

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Is Titu's lemma citeable without further explanation?

by turak, Jul 11, 2011, 7:06 AM

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It's equivalent to cauchy, so cite that.

On a sidenote this problem and solution are hilarious.

by pythag011, Jul 11, 2011, 7:45 AM

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