$n\geq2$ be an integer
Prove $|\sqrt[n]{a}-\sqrt[n]{b}|\le\sqrt[n]{|a-b|}$ for all $a,b\geq0$
I try taking both side n squared and using binomial theorem, but I can't prove it.
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I don't know how to answer your question, but I think $x$ and $y$ should be $a$ and $b$. – soupless Mar 22 '21 at 17:24
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This has been asked and answered before, e.g. here: https://math.stackexchange.com/q/2992987/42969 – Martin R Mar 22 '21 at 17:24
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5Please flag as a duplicate: How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$ – vitamin d Mar 22 '21 at 17:25
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Thanks. I should have searched variant x,y not a, b – XX X Mar 22 '21 at 17:32