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Inverse third order equation

  1. Apr 21, 2008 #1
    I have a question about solving a formula.

    I have a set of data which I have fit to an inverse third order equation, if I swap the axes (use X as Y and vise versa), R2 suffers dramatically but I would like to calculate both Y and X values independantly. I am wondering what the solution for the following equation is when cast to calculate X. My algebra is a little rusty and I am not sure where to start.

    y = y[tex]_{0}[/tex]+[tex]\frac{a}{x}[/tex]+[tex]\frac{b}{x^{2}}[/tex]+[tex]\frac{c}{x^{3}}[/tex]

    Assuming I have values for a,b,c, and yo, how do I solve this for x?
  2. jcsd
  3. Apr 21, 2008 #2
    Welcome to PF.

    Multiply the equation by x^3 and you get a polynomial of degree three, whose roots are given by "http://en.wikipedia.org/wiki/Cubic_function#Cardano.27s_method" [Broken].
    Last edited by a moderator: Apr 23, 2017 at 12:22 PM
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