Easy inequality
Source: 0
April 23, 2008
inequalitiesfunction
Problem Statement
IF , and are positive reals such that a^{2}\plus{}b^{2}\plus{}c^{2}\equal{}1 prove the inequality: \frac{a^{5}\plus{}b^{5}}{ab(a\plus{}b)}\plus{} \frac {b^{5}\plus{}c^{5}}{bc(b\plus{}c)}\plus{}\frac {c^{5}\plus{}a^{5}}{ca(a\plus{}b)}\geq 3(ab\plus{}bc\plus{}ca)\minus{}2.