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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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