See this:

https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means



and



https://math.stackexchange.com/questions/1298115/prove-inequality-abbcca-ge-3-abc-1






If you expand the left hand side you will get:



     = 



Expanding the middle gives:

     = 



Comparing term-by term, you get two inequalities to prove:

     

     



The LHS is a GM, the RHS is an AM,  so here the AM-GM inequality applies.



The middle term compared to the RHS (in original problem statement) is then proven in a similar fashion.





 

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