I am using a different method here.Originally Posted by Nichelle14
I am trying to prove that for any real numbers a,b,c the follwing inequality holds:
(a^2 + b^2 + c^2)/3 >= ((a+b+c)/3)^2
I multiplied out the square on the RHS and simplified.
Then got rid of the fraction on each side.
But what do I do next?
If x denotes a sequence of numbers, and AM(x) its arithmetic mean, you're being asked to prove that AM(f(x)) >= f(AM(x)) where f is squaring and f(x) means the sequence of values of f applied to the elements of x. You could prove this using only the fact that f is convex (f' and f'' both positive).