Prove that for any three distinct positive real numbers a, b and c:
((a^2 - b^2)^3 + (b^2 - c^2)^3 + (c^2 - a^2)^3
----------------------------------------------------------- > 8abc
(a-b)^3 + (b-c)^3 + (c-a)^3
(where dotted line shows it is a fraction)
I have no idea what to do here, help!!
Wait, first of all i dont know how to prove that. But, wouldn't (coming back to my question) it end up (a+b)/2 x (b+c)/2 x (c+a)/2 = sqr ab x sqr bc x sqr ca ?? (using AM>GM inequality) I need to get this done by tomorrow so yeah.
If x+y+z=0,show that x3+y3+z3=3xyz? - Yahoo! Answers India
read this too.