MathDB
Inequality with 2n variables

Source: Baltic Way 1992 #13

February 18, 2009
inequalitiesinequalities proposed

Problem Statement

Prove that for any positive x1,x2,…,xn,y1,y2,…,yn x_1,x_2,\ldots,x_n,y_1,y_2,\ldots,y_n the inequality \sum_{i\equal{}1}^n\frac1{x_iy_i}\ge\frac{4n^2}{\sum_{i\equal{}1}^n(x_i\plus{}y_i)^2} holds.
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