*Problem:*

If prove that

.

*Solution:*

From the well-known lemma we deduce that:

.

Doing that cyclic for and adding up the relations we get that

.

So, it is enough to prove that

.

Squaring both sides we come to the conclusion

, *Q.E.D.*

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*Related*

An other solutions is Minkowski’s inequality!! Just reduce to my lemma:

http://www.artofproblemsolving.com/blog/75446

😀