Problem #PRU-61392

Problems Algebra Algebraic inequalities and systems of inequalities Classical inequalities

Problem

We are given rational positive numbers \(p, q\) where \(1/p + 1/q = 1\). Prove that for positive \(a\) and \(b\), the following inequality holds: \(ab \leq \frac{a^p}{p} + \frac{b^q}{q}\).