Ukraine 2008
Source: Ukrainian TST 2008 Problem 3
July 30, 2008
inequalitiesinequalities proposed109
Problem Statement
For positive prove that
(a \plus{} b)(b \plus{} c)(c \plus{} d)(d \plus{} a)(1 \plus{} \sqrt [4]{abcd})^{4}\geq16abcd(1 \plus{} a)(1 \plus{} b)(1 \plus{} c)(1 \plus{} d)