- #1

- 2,020

- 1

## Homework Statement

Let p and q be positive real numbers such that

1/p + 1/q=1

Prove that if [itex]u\geq 0[/itex] and [itex]v \geq 0[/itex], then

[tex]uv \leq \frac{u^p}{p}+\frac{v^q}{q}[/tex]

## Homework Equations

## The Attempt at a Solution

I am really stumped. Is there like a famous inequality that I need to use here that I am forgetting?

This vaguely reminds me of the AM-GM inequality...