IMO Shortlist 1983 problem 9
Dodao/la:
arhiva2. travnja 2012. Let
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
,
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
and
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
be the lengths of the sides of a triangle. Prove that
Determine when equality occurs.
%V0
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