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Roots of implicit equations

  1. Jan 30, 2009 #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. Jan 30, 2009 #2
    I don't think that can be solved analytically, numerical approximations are the best you can get.
  4. Jan 30, 2009 #3


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

    To 500 decimal places:
  5. Jan 31, 2009 #4
    How did you get an answer to 500 decimal places?!
  6. Feb 1, 2009 #5
    Mathematica (for example) can do it.
  7. Feb 1, 2009 #6


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

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