Positive Real Numbers Such That (a^2 + b^2 + c^2 + d^2) = 1
Source: Irish Mathematical Olympiad - Paper 1 - 2008 -Question 2
May 10, 2008
inequalities proposedinequalities
Problem Statement
For positive real numbers , , and such that a^2 \plus{} b^2 \plus{} c^2 \plus{} d^2 \equal{} 1 prove that
a^2b^2cd \plus{} \plus{}ab^2c^2d \plus{} abc^2d^2 \plus{} a^2bcd^2 \plus{} a^2bc^2d \plus{} ab^2cd^2 \le 3/32,
and determine the cases of equality.