Inequality - GM, AM, HM and SM means
I've got stuck at this problem :
Prove that for any and any the following inequality is true:
The first thing that I've thought was the AM-GM inequality (the extended version - heard that is also known as The power mean inequality):
where , , , and refer to the harmonic, geometric, arithmetic, and square mean, respectively. CBS(Cauchy - Buniakowsky - Schwartz) also come to my mind, but I think it isn't helpful in this case.
I would be greatful for some hints.