Inequality with condition a + b + c = 1
Source: Austrian Mathematical Olympiad 2008 Problem 1
February 6, 2009
inequalitiesfunctionlogarithmsinequalities unsolved
Problem Statement
Prove the inequality
\sqrt {a^{1 \minus{} a}b^{1 \minus{} b}c^{1 \minus{} c}} \le \frac {1}{3}
holds for all positive real numbers , and with a \plus{} b \plus{} c \equal{} 1.