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2004 IMO Shortlist Problems/A5

Revision as of 20:57, 3 May 2015 by Yimingz89 (talk | contribs) (Created page with "== Problem == If <math>a,b,c</math> are three positive real numbers such that <math>ab+bc+ca=1</math>, prove <math><cmath> \sqrt[3]{\frac{1}{a}+6b}+\sqrt[3]{\frac{1}{b}+6c}+\s...")
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Problem

If $a,b,c$ are three positive real numbers such that $ab+bc+ca=1$, prove $<cmath> \sqrt[3]{\frac{1}{a}+6b}+\sqrt[3]{\frac{1}{b}+6c}+\sqrt[3]{\frac{1}{c}+6a}\le\frac{1}{abc}. </cmath>$

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