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\frac{a^2+b^2}{c}+\frac{b^2+c^2}{a}+\frac{c^2+a^2}{b}>0 if abc<0, a+b+c=0

Source: Caucasus 2015 8.4

April 26, 2019
algebrainequalitiesthree variable inequality

Problem Statement

The sum of the numbers a,ba,b and cc is zero, and their product is negative. Prove that the number a2+b2c+b2+c2a+c2+a2b\frac{a^2+b^2}{c}+\frac{b^2+c^2}{a}+\frac{c^2+a^2}{b} is positive.
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