**Reference: R. Todev, Nordic Mathematical Contests, 1987-2009.**

**Question:**

Let a, b, and c be positive real numbers. Prove that .

**Solution:**

The arithmetic-geometric inequality yields

,

or …call this relation I.

On the other hand, the Cauchy-Schwarz inequality implies

….call this relation II.

We arrive at the inequality we desire by combining relations I and II. Hence, the proof. QED.

Cheers,

Nalin Pithwa.

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