MathDB
Inequality

Source: Albania IMO TST 2013

May 25, 2013
inequalitiesrearrangement inequalityinequalities proposed

Problem Statement

Let a,b,c,da,b,c,d be positive real numbers such that abcd=1abcd=1.Find with proof that x=3x=3 is the minimal value for which the following inequality holds: ax+bx+cx+dx≥1a+1b+1c+1da^x+b^x+c^x+d^x\ge\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}+\dfrac{1}{d}
Back to ProblemsView on AoPS