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Daca a, b, c > 0, sa se demonstreze inegalitatea
\( \frac{1}{2a} + \frac{1}{2b} + \frac{1}{2c} \geq \frac{1}{a+b} + \frac{1}{b+c} + \frac{1}{c+a} \)

Cauchy:

\(
\frac{1}{a}+\frac{1}{b}\ge \frac{4}{a+b} \)

si adunand analoagele rezulta concluzia.