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== | ||
| − | + | {{solution}} | |
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{IMO box|year=2006|num-b=2|num-a=4}} | ||
Latest revision as of 00:03, 19 November 2023
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
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See Also
| 2006 IMO (Problems) • Resources | ||
| Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
| All IMO Problems and Solutions | ||
