USAMO 2003 Problem 5
Source:
September 27, 2005
AMCUSA(J)MOUSAMOinequalitiesfunctioncalculus
Problem Statement
Let , , be positive real numbers. Prove that
\dfrac{(2a \plus{} b \plus{} c)^2}{2a^2 \plus{} (b \plus{} c)^2} \plus{} \dfrac{(2b \plus{} c \plus{} a)^2}{2b^2 \plus{} (c \plus{} a)^2} \plus{} \dfrac{(2c \plus{} a \plus{} b)^2}{2c^2 \plus{} (a \plus{} b)^2} \le 8.