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Equation solving

  1. Dec 28, 2011 #1

    I want to solve the following equation by x:

    Ʃ(ai^x -b)^2 = C ,
    where Ʃ is over all i, i = 1:N, and ^ means "to the power of"

    How to find x from here?

  2. jcsd
  3. Dec 28, 2011 #2


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    Staff: Mentor

    Welcome to the PF.

    What is the context of the question? Is it from schoolwork?
  4. Dec 29, 2011 #3
    Try expanding the quadratic that's in the sum. Then you should ultimately be able to turn it into one quadratic equation.
  5. Dec 29, 2011 #4


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    Science Advisor
    Homework Helper

    It isn't a quadratic. The equation is [itex]\sum(a_i^x -b)^2 = C[/itex] , not [itex]\sum(a_ix -b)^2 = C[/itex]
  6. Dec 29, 2011 #5
    Ah my mistake. Thanks a lot.
  7. Dec 29, 2011 #6
    it is not the homework, it's more like a part of a research problem.. my algebra class was long time ago.
  8. Jan 4, 2012 #7
    Anyone has a clue?
  9. Jan 4, 2012 #8
    If you want an analytical solution for the general case, I'd say (pretty confidently) that it just can't be done. If you have specific values for the a_i, then I'd try it numerically.
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