1964 IMO Problems/Problem 2

Revision as of 19:33, 15 July 2009 by Xpmath (talk | contribs) (Created page with '== Problem == Suppose <math>a, b, c</math> are the sides of a triangle. Prove that <cmath>a^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le{3abc}.</cmath> == Solution ==')
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Problem

Suppose $a, b, c$ are the sides of a triangle. Prove that

\[a^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le{3abc}.\]

Solution

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