37th Austrian Mathematical Olympiad 2006
Source: round 3, day1, problem 2
February 10, 2009
inequalities unsolvedinequalities
Problem Statement
Let be positive real numbers. Show that
3(a \plus{} b \plus{} c) \ge 8 \sqrt [3]{abc} \plus{} \sqrt [3]{\frac {a^3 \plus{} b^3 \plus{} c^3}{3} }.