**Problem**

Let . Prove that:

**Proof**

By C-S ,

Thus it is sufficient to prove that (after removing in the denominators)-

Let ,

The inequality is transformed into –

By AM-GM ,

Thus it is sufficient to prove that –

By Schur’s Inequality we know that –

Thus it is left to prove that –

This is equivalent to –

Hence Proved with equality when all the variables are equal 🙂

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