Unusal inequality
Source: from Vietnam olympiad 1999
January 21, 2006
inequalitiestrigonometryinequalities unsolvedalgebra
Problem Statement
Given are three positive real numbers satisfying abc \plus{} a \plus{} c \equal{} b. Find the max value of the expression:
P \equal{} \frac {2}{a^2 \plus{} 1} \minus{} \frac {2}{b^2 \plus{} 1} \plus{} \frac {3}{c^2 \plus{} 1}.