## Prove that there exists an x such that x[SUP]3[/SUP] = 2

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

Prove that there exists an x such that x3 = 2

2. Relevant equations

3. The attempt at a solution

I have deduced in an earlier part of the question, using the intermediate value theorem, that every monic polynomial of odd degree has a real root.

So if I consider x3 - 2 = 0, as a monic polynomial of odd degree, I know that it has a real root. Can I just say that this is the x that I am looking for? I don't feel like I've really proved it fully.

Mentor
 Quote by Kate2010 1. The problem statement, all variables and given/known data Prove that there exists an x such that x3 = 2 2. Relevant equations 3. The attempt at a solution I have deduced in an earlier part of the question, using the intermediate value theorem, that every monic polynomial of odd degree has a real root. So if I consider x3 - 2 = 0, as a monic polynomial of odd degree, I know that it has a real root. Can I just say that this is the x that I am looking for? I don't feel like I've really proved it fully.
Based on your problem statement, all you need to show is existence, and the previous work you did shows that for this polynomial.
 If all you have to do is prove the existence of such an x then why don't you simply find x, which isn't very difficult. Unless there is something I'm missing.