Let a,b,c be positive real numbers such that ab\plus{}bc\plus{}ca\equal{}3. Prove that
\frac 1{1\plus{}a^2(b\plus{}c)} \plus{} \frac 1{1\plus{}b^2(c\plus{}a)} \plus{} \frac 1 {1\plus{}c^2(a\plus{}b) } \leq \frac 3 {1\plus{}2abc} . inequalitiesfunctionparameterizationalgebrapolynomialVietaCauchy Inequality