MathDB

Inequalities

Source: Federal Mathematical Competition of Serbia and Montenegro 2004

May 14, 2018

inequalities

Problem Statement

a,b,c

are positive numbers such that

abc = 1

, prove the inequality

\frac{1}{\sqrt{b+\frac{1}{a}+\frac{1}{2}}} + \frac{1}{\sqrt{c+\frac{1}{b}+\frac{1}{2}}} + \frac{1}{\sqrt{a+\frac{1}{c}+\frac{1}{2}}} \geq \sqrt{2}