An inequality with condition a+b+c=1.
Source: 40th Canadian Mathematical Olympiad
April 21, 2008
inequalitiestrigonometryinequalities proposedalgebra
Problem Statement
Let , , be positive real numbers for which a \plus{} b \plus{} c \equal{} 1. Prove that
{{a\minus{}bc}\over{a\plus{}bc}} \plus{} {{b\minus{}ca}\over{b\plus{}ca}} \plus{} {{c\minus{}ab}\over{c\plus{}ab}}
\leq {3 \over 2}.