2004 IMO Shortlist Problems/A5: Difference between revisions
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..." |
|||
| Line 1: | Line 1: | ||
== Problem == | == 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}+\sqrt[3]{\frac{1}{c}+6a}\le\frac{1}{abc}. </cmath></math> | 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}+\sqrt[3]{\frac{1}{c}+6a}\le\frac{1}{abc}. </cmath></math> | ||
== Solution == | |||
https://youtu.be/jmXSmmfO7pQ?si=dxJ6At7KHlcn2NT5 [Video Solution by little fermat] | |||
Latest revision as of 10:20, 26 September 2024
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)
Solution
https://youtu.be/jmXSmmfO7pQ?si=dxJ6At7KHlcn2NT5 [Video Solution by little fermat]
