Problem

Source: Caucasus 2015 8.4

Tags: algebra, inequalities, three variable inequality



The sum of the numbers $a,b$ and $c$ is zero, and their product is negative. Prove that the number $\frac{a^2+b^2}{c}+\frac{b^2+c^2}{a}+\frac{c^2+a^2}{b}$ is positive.