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1983 IMO Problems/Problem 6

Revision as of 16:32, 22 August 2017 by Neep (talk | contribs) (Created page with "==Problem 6== Let <math>a</math>, <math>b</math> and <math>c</math> be the lengths of the sides of a triangle. Prove that <math>a^2 b(a-b) + b^2 c(b-c) + c^2 (c-a) \geq 0</ma...")
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Problem 6

Let $a$, $b$ and $c$ be the lengths of the sides of a triangle. Prove that

$a^2 b(a-b) + b^2 c(b-c) + c^2 (c-a) \geq 0$.

Determine when equality occurs.

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