Problem

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2010

Tags: algebra, inequalities



Prove the inequality $$ \frac{y^2-x^2}{2x^2+1}+\frac{z^2-y^2}{2y^2+1}+\frac{x^2-z^2}{2z^2+1} \geq 0$$where $x$, $y$ and $z$ are real numbers