# Inequality

• March 19th 2011, 02:38 PM
Berge
Inequality
how to prove that :

$

\noindent\(|x^3-p^3|\leq \ 7p^2 |x-p| \ if \noindent\ |x|\leq |2p|
$
• March 19th 2011, 03:18 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.