Triangle proof

[MeiKageyama]

Proof for the general triangle which sides have length a,b,c that:




I was thinking of taking this for one side and unjumble it or taking something before the round bracket and then proof that everything is equal more than zero but I don't know what to do with these letters under the square root.

 

[topsquark]

As all of a, b, and c are positive start by squaring:
[imath]4(a^2 + b^2 + c^2) < 3(a + b + c)^2[/imath]

What can you do from here?

-Dan