MathDB
3 variables with condition ab+bc+ca=1

Source: Korea National Olympiad 2010 Problem 2

September 9, 2012
inequalitiesinequalities proposed

Problem Statement

Let a,b,c a, b, c be positive real numbers such that ab+bc+ca=1 ab+bc+ca=1 . Prove that a2+b2+1c2+b2+c2+1a2+c2+a2+1b2≥33 \sqrt{ a^2 + b^2 + \frac{1}{c^2}} + \sqrt{ b^2 + c^2 + \frac{1}{a^2}} + \sqrt{ c^2 + a^2 + \frac{1}{b^2}} \ge \sqrt{33}
Back to ProblemsView on AoPS