olymmath

JBMO-SL 2004 A2

    Prove that, for all real numbers x,y,zx, y, z :

    x2−y22x2+1+y2−z22y2+1+z2−x22z2+1≤(x+y+z)2\frac{x^{2}-y^{2}}{2 x^{2}+1}+\frac{y^{2}-z^{2}}{2 y^{2}+1}+\frac{z^{2}-x^{2}}{2 z^{2}+1} \leq(x+y+z)^{2}

    When the equality holds?

    Dataset text NuminaMath olympiads. Quoted with source.

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