IMO ShortList 2008, Algebra problem 5
Source: IMO ShortList 2008, Algebra problem 5, German TST 1, P3, 2009
July 9, 2009
inequalitiesalgebraIMO Shortlist
Problem Statement
Let , , , be positive real numbers such that abcd \equal{} 1 and a \plus{} b \plus{} c \plus{} d > \dfrac{a}{b} \plus{} \dfrac{b}{c} \plus{} \dfrac{c}{d} \plus{} \dfrac{d}{a}. Prove that
a \plus{} b \plus{} c \plus{} d < \dfrac{b}{a} \plus{} \dfrac{c}{b} \plus{} \dfrac{d}{c} \plus{} \dfrac{a}{d}
Proposed by Pavel Novotný, Slovakia