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: $a b \leq \frac{a^{p}}{p} + \frac{b^{q}}{q}$ .

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