MathDB

1

Part of 1962 Vietnam National Olympiad

Problems(1)

Inequality for positive real numbers

Source: Vietnam NMO 1962 Problem 1

2/1/2009
Prove that for positive real numbers a a, b b, c c, d d, 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}}
inequalities