Roots of implicit equations

  1. I was working on double integrals when I came across the equation: x^(3/2)=sin(x).
    There was no noticeable way to isolate the equation for x without having a function of x equal to x. I am wondering how to isolate equations involving logs, sines, etc when it is given in an implicit form.
    Using a computer, I was able to get an approximation of 0 and 8.02... How do I get the EXACT value of x?
  2. jcsd
  3. I don't think that can be solved analytically, numerical approximations are the best you can get.
  4. CRGreathouse

    CRGreathouse 3,497
    Science Advisor
    Homework Helper

    There's no reason to expect a nice solution to that equation.

    To 500 decimal places:
  5. How did you get an answer to 500 decimal places?!
  6. Mathematica (for example) can do it.
  7. arildno

    arildno 11,265
    Science Advisor
    Homework Helper
    Gold Member

    What's wrong with x=0 as an exact solution??
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