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Thread: Inequality

  1. #1
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    Inequality

    how to prove that :

    $\displaystyle

    \noindent\(|x^3-p^3|\leq \ 7p^2 |x-p| \ if \noindent\ |x|\leq |2p|
    $
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  2. #2
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    Quote Originally Posted by Berge View Post
    how to prove that :
    $\displaystyle \noindent\(|x^3-p^3|\leq \ 7p^2 |x-p| \ if \noindent\ |x|\leq |2p|$
    Recall that $\displaystyle x^3-p^3=(x-p)(x^2+xp+p^2)$

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

    Show us what you can do with that.
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