39th Austrian Mathematical Olympiad
Source: round1, problem1
February 10, 2009
inequalitiesinequalities unsolved
Problem Statement
Show: For all real numbers with is:
\sqrt{a^2bc\plus{}ab^2c\plus{}abc^2}\plus{}\sqrt{(1\minus{}a)^2(1\minus{}b)(1\minus{}c)\plus{}(1\minus{}a)(1\minus{}b)^2(1\minus{}c)\plus{}(1\minus{}a)(1\minus{}b)(1\minus{}c)^2}<\sqrt{3}.