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Regional Olympiad - FBH 2010 Grade 11 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2010

September 27, 2018
algebrainequalities

Problem Statement

Prove the inequality y2−x22x2+1+z2−y22y2+1+x2−z22z2+1≥0 \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 xx, yy and zz are real numbers
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