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 < | + | Determine the least real number <math>M</math> such that the inequality <cmath> \left| ab\left(a^{2}-b^{2}\right)+bc\left(b^{2}-c^{2}\right)+ca\left(c^{2}-a^{2}\right)\right|\leq M\left(a^{2}+b^{2}+c^{2}\right)^{2} </cmath> holds for all real numbers <math>a,b</math> and <math>c</math> |
==Solution== | ==Solution== | ||
. | . | ||
Revision as of 02:51, 19 July 2015
Problem
Determine the least real number 
such that the inequality ![\[\left| ab\left(a^{2}-b^{2}\right)+bc\left(b^{2}-c^{2}\right)+ca\left(c^{2}-a^{2}\right)\right|\leq M\left(a^{2}+b^{2}+c^{2}\right)^{2}\]](http://latex.artofproblemsolving.com/8/d/d/8dde3f3a2bba98bb6c84ef65230d69a2ded149cc.png)
holds for all real numbers 
and 
Solution
.
