MathDB
Inequality, Problem 2

Source: Kazakhstan National Olympiad 2017, March 14, P2 , matol.kz

March 15, 2017
Kazakhstan2017inequalities

Problem Statement

For positive reals x,y,z≥12x,y,z\ge \frac{1}{2} with x2+y2+z2=1x^2+y^2+z^2=1, prove this inequality holds
(1x+1y−1z)(1x−1y+1z)≥2(\frac{1}{x}+\frac{1}{y}-\frac{1}{z})(\frac{1}{x}-\frac{1}{y}+\frac{1}{z})\ge 2
Back to ProblemsView on AoPS