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Help Solving a Quartic Polynomial

  1. Apr 24, 2013 #1
    I am trying to solve an equation:

    arccos(Y) = arctan(Y), where Y = 1/x

    This turns into a quartic equation:

    x4 - x2 - 1 = 0

    It looks simple enough to simplify further; however, I must be having a brain-fart because I can't do it. I'd like to avoid resorting to a numerical solution.

    Am I overlooking something?
    Can this equation be simplified further? If so, how?

    Any help is much appreciated.
  2. jcsd
  3. Apr 24, 2013 #2
    Setting [itex]u = x^2[/itex], you can rewrite it as [itex]u^2 - u - 1 = 0[/itex]. You can solve this easily enough for the roots in u, and then solve the roots for x.
  4. Apr 24, 2013 #3

    Thank-you very much!
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