Question 13
Let $a$, $b$ and $c$ be the lengths of the sides of a triangle. Demonstrate that $$
a^{2} b(a-b) + b^{2} c(b-c) + c^{2} a(c-a) \geq 0
$$ determine in which cases the equality is met.
a^{2} b(a-b) + b^{2} c(b-c) + c^{2} a(c-a) \geq 0
$$ determine in which cases the equality is met.