Question

Prove that in a triangle (a+b+c) ^3>27(a+b-c)(b+c-a)(c,+a-b)

Answer 1

three sectors of a circle of radius 7cm making angles of 60 , 80 and 40 at the centre are shaded. what is the area of the shaded region?

Answer 2

I have tried the arithmetic-geometric inequality on (−a+b+c)(a−b+c)(a+b−c)which gives
(−a+b+c)(a−b+c)(a+b−c)≤(a+b+c3)3
and on abc which gives
abc≤(a+b+c3)3.
Since both inequalities have the same righthand side, I have tried to deduce something about the lefthand sides, but to no avail. Can somebody help me, please? I am sure it is something simple I have missed.