antiemptyv
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Homework Statement
Let a>b>0 and let n \in \mathbb{N} satisfy n \geq 2. Prove that a^{1/n} - b^{1/n} < (a-b)^{1/n}.
[Hint: Show that f(x):= x^{1/n}-(x-1)^{1/n} is decreasing for x\geq 1, and evaluate f at 1 and a/b.]
Homework Equations
I assume, since this exercise is at the end of the Mean Value Theorem section, I am to use the Mean Value Theorem.
The Attempt at a Solution
I can show what the hint suggests. I guess I'm not sure how those ideas help exactly.