How do you prove
(a+b+c)/3 greater than or equal to the cubed root of (abc)
I keep getting people show me answers for the case of 2 numbers, this is nice but l already know how to do that and would really appreciate if someone would show me how to figure it out for 3
cube both sides, take RHS over and prove greater than zero is the way l can see it, but is there some algebraic trick after that l am not seeing
short of proving by induction l don't know how else to do it
Serious response please
(a+b+c)/3 greater than or equal to the cubed root of (abc)
I keep getting people show me answers for the case of 2 numbers, this is nice but l already know how to do that and would really appreciate if someone would show me how to figure it out for 3
cube both sides, take RHS over and prove greater than zero is the way l can see it, but is there some algebraic trick after that l am not seeing
short of proving by induction l don't know how else to do it
Serious response please