MathDB
\sum (x_i +y_i)^2 \sum 1/x_iy_i >= 4n^2

Source: Norwegian Mathematical Olympiad 1995 - Abel Competition p4

February 11, 2020
inequalitiesalgebra

Problem Statement

Let xi,yix_i,y_i be positive real numbers, i=1,2,...,ni = 1,2,...,n. Prove that (∑i=1n(xi+yi)2)(∑i=1n1xiyi)≥4n2\left( \sum_{i=1}^n (x_i +y_i)^2\right)\left( \sum_{i=1}^n\frac{1}{x_iy_i}\right)\ge 4n^2
Back to ProblemsView on AoPS