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>
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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 19:30, 8 April 2015

Problem

Determine the least real number $M$ 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 $a,b$ and $c$

Solution

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