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

  1. Jan 31, 2010 #1
    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.
  2. jcsd
  3. Jan 31, 2010 #2


    Staff: Mentor

    Based on your problem statement, all you need to show is existence, and the previous work you did shows that for this polynomial.
  4. Jan 31, 2010 #3
    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.
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