Help Solving a Quartic Polynomial

  • Thread starter DuncanM
  • Start date
  • #1
98
2
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.
 

Answers and Replies

  • #2
806
23
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.
 
  • #3
98
2
Excellent!

Thank-you very much!
 

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