Problem #PRU-61411

Problems Algebra and arithmetic Algebraic inequalities and systems of inequalities Algebraic inequalities (other)

Problem

Let $p$ and $q$ be positive numbers where $1 / p + 1 / q = 1$ . Prove that $a_{1} b_{1} + a_{2} b_{2} + \dots + a_{n} b_{n} \leq (a_{1}^{p} + \dots a_{n}^{p})^{1 / p} (b_{1}^{q} + \dots + b_{n}^{q})^{1 / q}$ The values of the variables are considered positive.

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