# Difference between revisions of "2006 IMO Problems/Problem 3"

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==Problem== | ==Problem== | ||

− | Determine the least real number <math>M</math> such that the inequality <math> \left|ab\left(a^{2}-b^{2}\right)+bc\left(b^{2}-c^{2}\right)+ca\left(c^{2}-a^{2}\right)|\leq M\left(a^{2}+b^{2}+c^{2}\right)^{2} </math> holds for all real numbers <math>a,b</math> and <math>c</math> | + | Determine the least real number <math>M</math> such that the inequality <math> \left|ab\left(a^{2}-b^{2}\right)\right+bc\left(b^{2}-c^{2}\right)+ca\left(c^{2}-a^{2}\right)|\leq M\left(a^{2}+b^{2}+c^{2}\right)^{2} </math> holds for all real numbers <math>a,b</math> and <math>c</math> |

==Solution== | ==Solution== | ||

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## Revision as of 20:30, 8 April 2015

## Problem

Determine the least real number such that the inequality $\left|ab\left(a^{2}-b^{2}\right)\right+bc\left(b^{2}-c^{2}\right)+ca\left(c^{2}-a^{2}\right)|\leq M\left(a^{2}+b^{2}+c^{2}\right)^{2}$ (Error compiling LaTeX. ! Missing delimiter (. inserted).) holds for all real numbers and

## Solution

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