Edit: Oh never mind - I think that's just 0.
Edit 2: Lol. Oh yeah - that's why it works.
Assuming that a,b and c are positif real numbers .
Using the Arithmetic mean-Geometric mean inequality we get a˛+b˛>=2ab also a˛+c˛>=2ac and b˛+c˛>=2bc summing we get a˛+b˛+c˛>=ab+ac+bc and equality holds in this inequality when a=b=c !
You can also use the Cauchy-Schwartz inequality and in the same way you get equality holds when a=b=c
I believe something similar was posted before:
Thanks for all, the replies, but all your solutions make use of the fact that a, b, c are positive. There is no word of it in the original wording I have got, and without that I don't think you can sum inequalities together or draw a concluion Archie Meade has done... maybe there is a problem with the phrasing of the question and a, b, c should indeed be positive?