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## Homework Statement

for reals x and y with x greater than y, prove that n*x^(n-1)(x-y)>=x^n-y^n for n>0.

## Homework Equations

## The Attempt at a Solution

Let p(n) be that the statement is true for some n.

base case: obviously follows

inductive step: assume p(k) is true for some k.

Look at (n+1)x^(n-1+1)(a-b) = (n*x^n+x^n)(x-y)

= n*x*x^n - n*y*x^n+x*x^n-y*x^n

I'm stuck here. I know there is a way to do it using the property (x^n-y^n) = (x-y)(some polynomial), but we were specifically asked not to use that and to do it by induction.