Let be positive real numbers such that . Prove that

**Solution**

Well if we apply AM-GM to we obtain

(1)

and similarly if we apply AM – GM to we obtain

(2)

We have successively,

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Let be positive real numbers such that . Prove that

**Solution**

Well if we apply AM-GM to we obtain

(1)

and similarly if we apply AM – GM to we obtain

(2)

We have successively,