MathDB
Iran TST 2009-Day1-P3

Source:

May 9, 2009
calculusfunctionthree variable inequalityalgebraInequality

Problem Statement

Suppose that a a,b b,c c be three positive real numbers such that a\plus{}b\plus{}c\equal{}3 . Prove that : \frac{1}{2\plus{}a^{2}\plus{}b^{2}}\plus{}\frac{1}{2\plus{}b^{2}\plus{}c^{2}}\plus{}\frac{1}{2\plus{}c^{2}\plus{}a^{2}} \leq \frac{3}{4}