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Constructible angles->help please

  1. Apr 8, 2009 #1
    constructible angles-->help please

    1. The problem statement, all variables and given/known data

    x=2(pi)/7 we will show that this is not constructible and therefore 7-gon is not constructible.

    a) show cos4x = cos3x
    b) Use the above equation to find a rational quartic polynomial f(y)
    where f(cos x) = 0.
    c)From f, find a cubic rational polynomial g(y) where g(cos x) = 0

    2. Relevant equations

    see above

    3. The attempt at a solution

    im having trouble in part b). i expanded cos4x - cos3x = 0 in terms of cos(x) and I made the substitution y= cos(x) i got the quartic equation 8y^4 + 4y^3 - 8y^(2) -3y + 1 =0.
    but when i put y= cos(2(pi)/7)) it dosent come out to 0.
     
  2. jcsd
  3. Apr 8, 2009 #2
    Re: constructible angles-->help please

    You found cos 4x + cos 3x instead of minus. LOL, I made the same error.
     
  4. Apr 8, 2009 #3
    Re: constructible angles-->help please

    oh right it should be -4 and +3 in the above equation, thanks billy do u know how to change this into a cubic equation.
     
  5. Apr 8, 2009 #4
    Re: constructible angles-->help please

    Try long division? Divide by y-c, where c is a root of the quartic. Hopefully c is easy to find, by graphing, or guessing.
     
  6. Apr 8, 2009 #5
    Re: constructible angles-->help please

    i tried doing that the root is 1 so i divided it by y-1 im getting 8y^3 + 4y^2 - 4y +7 + some remainder???
     
  7. Apr 8, 2009 #6
    Re: constructible angles-->help please

    oh i got it, thank you
     
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