For are positive reals.

Prove that

.

**Proof**

Let ,

Thus ,

substituting in the question we have –

and,

By AM-GM ,

$latex \sum \frac {ac}{2} \le \sum \frac {a^2}{2} = LHS$

and we are done.

With equality for

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Where numbers speak …

For are positive reals.

Prove that

.

**Proof**

Let ,

Thus ,

substituting in the question we have –

and,

By AM-GM ,

$latex \sum \frac {ac}{2} \le \sum \frac {a^2}{2} = LHS$

and we are done.

With equality for

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