# Finding trigonometric solution to a cubic equation using computer

1. Nov 18, 2013

### Seydlitz

Hello,

1. The problem statement, all variables and given/known data
I get this question from Mathematical Methods by Boas page 74 problem 25. The question states:

"Use a computer to find the three solutions of the equation $x^3-3x-1=0$. Find a way to show that the solutions can be written as $2cos(\frac{\pi}{9})$, $-2cos(\frac{2\pi}{9})$, $2cos(\frac{4\pi}{9})$.

3. The attempt at a solution
Again I'm still confused on what she means by use a computer?

Can I just use Wolfram Alpha to find the solution in exact form and then show it that it can be expressed to polar form and hence trigonometric function? I checked with WA and it gives me the solution x in rectangular form. I just convert that to trigonometric form and it does get the same answer as the question.

But then on the other hand, the question itself was probably written long before program such as WA existed. Should I just skip this kind of problem next time?

Thank You