Difference between revisions of "2004 IMO Shortlist Problems/A5"
(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...") |
(No difference)
|
Latest revision as of 20:57, 3 May 2015
Problem
If 
are three positive real numbers such that 
, prove ![$<cmath> \sqrt[3]{\frac{1}{a}+6b}+\sqrt[3]{\frac{1}{b}+6c}+\sqrt[3]{\frac{1}{c}+6a}\le\frac{1}{abc}. </cmath>$](http://latex.artofproblemsolving.com/6/e/0/6e031f6527ab4fe0df313963a1aa994ca54b2086.png)
