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Thread: Inequality

  1. March 19th 2011, 01:38 PM #1
    Berge
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    Inequality

    how to prove that :

    <br /> <br /> \noindent\(|x^3-p^3|\leq \ 7p^2 |x-p| \ if \noindent\ |x|\leq |2p|<br />
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  2. March 19th 2011, 02:18 PM #2
    Plato
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    Quote Originally Posted by Berge View Post
    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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