Inequality

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March 19th 2011, 01:38 PM
Berge

Inequality

how to prove that :

$<br /> <br /> \noindent\(|x^3-p^3|\leq \ 7p^2 |x-p| \ if \noindent\ |x|\leq |2p|<br />$
March 19th 2011, 02:18 PM
Plato

Quote:

Originally Posted by Berge

how to prove that :
$\noindent\(|x^3-p^3|\leq \ 7p^2 |x-p| \ if \noindent\ |x|\leq |2p|$

Recall that $x^3-p^3=(x-p)(x^2+xp+p^2)$

So $|x^2+xp+p^2|\le x^2+|x||p|+p^2$

Show us what you can do with that.

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