Suppose that a,b,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} calculusfunctionthree variable inequalityalgebraInequality