BALKAN-SL 2011 A1

Given real numbers $x,y,z$ such that $x+y+z=0$ , show that $\dfrac{x(x+2)}{2x^2+1}+\dfrac{y(y+2)}{2y^2+1}+\dfrac{z(z+2)}{2z^2+1}\ge 0$

When does equality hold?

Dataset text AoPS wiki problems. Quoted with source.

Solutions

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