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happyg1
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Homework Statement
Prove that it is possible to trisect 72 degrees.Homework Equations
[tex]cos(3\theta)=4cos^3(\theta)-3cos(\theta)[/tex]
The Attempt at a Solution
well,72/3=24, So I need to see if cos24 is constructible, Which means that it is a root of a polynomial with a degree that is a power of 2.(?)I think.I did this:[tex]cos(72)=\frac{\sqrt5-1}{4}[/tex]
and [tex]Let \theta=24[/tex]
so then letting [tex]cos\theta=x[/tex] in the equation above,
I get:
[tex](\sqrt5)=(16x^3+12x+1)[/tex]
Now I get a little confused about what I'm trying to do.
Here's what I need help with:
Firstly, am I on the right track here?
Secondly, Is the "degree of a power of 2" (above) correct?
What is it that I need to do with this polynomial from here?
I've confused myself.
CC
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