*Problem:*

Let and be real numbers. Prove the Inequality

*Solution:*

Without loss of generality, let us assume that . Then according to the *AM-GM *Inequality we have that

Therefore, it holds that

It remains now to prove that

which reduces to the obvious, after expansions, Inequality Equality holds if and only if or any cyclic permutations of the previous equality *Q.E.D.*

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