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Regional Olympiad - FBH 2014 Grade 10 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2014

September 24, 2018
algebrainequalities proposedInequality

Problem Statement

Let aa, bb and cc be positive real numbers such that ab+bc+ca=1ab+bc+ca=1. Prove the inequality: 1a+1b+1c≥3(a+b+c)\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \geq 3(a+b+c)
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