Let , and be the lengths of the sides of a triangle. Prove that Determine when equality occurs.
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Let $a$, $b$ and $c$ be the lengths of the sides of a triangle. Prove that
$$a^{2}b(a - b) + b^{2}c(b - c) + c^{2}a(c - a)\ge 0.$$
Determine when equality occurs.
Izvor: Međunarodna matematička olimpijada, shortlist 1983
Školjka 
, 
and 
be the lengths of the sides of a triangle. Prove that 