Inequality for positive real numbers
Source: Vietnam NMO 1962 Problem 1
February 1, 2009
inequalities
Problem Statement
Prove that for positive real numbers , , , , we have \frac{1}{\frac{1}{a}\plus{}\frac{1}{b}}\plus{}\frac{1}{\frac{1}{c}\plus{}\frac{1}{d}}\le\frac{1}{\frac{1}{a\plus{}c}\plus{}\frac{1}{b\plus{}d}}