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I An algebraic equation

  1. Nov 7, 2016 #1
    Hi,

    I'm currently studying percolation theory and here I'm stuck on the this "simple" algebraic equation
    [tex]ax^{n-1} - x +1 - a = 0[/tex]
    clearly, the trivial solution x = 1 solves it. But I'm told that
    [tex]x = 1 - \frac{2a(n-1)-2}{a(n-2)(n-1)}[/tex]
    is another solution. This makes we wonder, if the equation can be put into a simpler form (e.g. quadratic or cubic) — even though I haven't succeed to.

    Can any of you help ??

    Thaks in advance.
     
    Last edited by a moderator: Nov 7, 2016
  2. jcsd
  3. Nov 7, 2016 #2

    FactChecker

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    I don't think that the statement is true. With a=4, n=4, I get x=1/12 and f(1/12) = -1331/432
     
  4. Nov 7, 2016 #3

    Stephen Tashi

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    Then you can obtain an equation in a lower power of x by dividing the original equation by (x-1). Try that for a particular case like n = 3.
     
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