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How to solve cube roots question ?

  1. Aug 10, 2006 #1
    How to solve cube roots question ?
    Example :
    x^3 - 100x^2 - 7800x + 16300 = 0

    I had think long time but still cannot find the way. Besides trial an error, is there anyway to solve this problem ?
    thank you.
     
  2. jcsd
  3. Aug 10, 2006 #2
    There are numerical methods to get approximate solutions ...

    For an exact solution you may find useful this

    http://mizar.uwb.edu.pl/JFM/Vol12/polyeq_1.html" [Broken]
     
    Last edited by a moderator: May 2, 2017
  4. Aug 10, 2006 #3

    CRGreathouse

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  5. Aug 11, 2006 #4

    radou

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    For a given equation [tex]x^3+ax^2+bx+c=0[/tex], we can substitute [tex]x=y-\frac{a}{3}[/tex], which implies [tex]y^3+py+q=0[/tex], where [tex]p=b-\frac{a^2}{3}[/tex], and [tex]q=\frac{2a^3}{17}-\frac{ab}{3}+c[/tex]. After further manipulation, one can retrieve [tex]x=\sqrt[3]{-\frac{q}{2}+\sqrt{(\frac{q}{2})^2+(\frac{p}{3})^3}}+\sqrt[3]{-\frac{q}{2}-\sqrt{(\frac{q}{2})^2+(\frac{p}{3})^3}}[/tex], which represents Cardan's formula.
     
  6. Aug 13, 2006 #5
    thank guy ~
     
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