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Solve 3b^(2/3) - 2b = 10/16

  1. Jan 24, 2012 #1
    The problem statement, all variables and given/known data

    3b^(2/3) - 2b = 10/16

    Find solution to a precision of thousanths



    The attempt at a solution

    I know the answer is ~ .199, I do not however know how to actually solve the above equation. If anyone can help, I'd appreciate it, it's been over 10 years since I took an algebra class.
     
  2. jcsd
  3. Jan 24, 2012 #2

    SammyS

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    Reduce 10/16 → 5/8.

    Isolate the 3b2/3 by adding 2b to both sides.

    Cube both sides.

    The result is a cubic equation. This particular cubic equation does not have any rational solutions.

    Use the bisection method, starting with a very small interval near 0.2. There is the solution near 0.2, as you said, but there's another nearby; between -0.1 and 0 .

    There is a third solution that's between 2 and 3.
     
  4. Jan 24, 2012 #3
    I believe Newton-Rhapsody iterative solving method might help you to find the roots if they are real ofcourse:

    http://en.wikipedia.org/wiki/Newton's_method
     
  5. Jan 24, 2012 #4
    Thanks guys,

    This was the end of a much larger problem and it now makes sense that I need to use the Newton's Method(this is was the end of a Calc II) problem.

    It's been a long time for some algebra concepts for me so I appreciate all the help.

    Dave
     
  6. Jan 24, 2012 #5

    SammyS

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    This is the pre-calculus section, so I suggested bisection.

    Make sure your initial guess is close enough to the root you want to find. Newton's Method may find a different root if you don't start close enough to the one you're interested in.
     
  7. Jan 24, 2012 #6

    Mark44

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    There's Newton-Raphson, which is probably what you were thinking of.
     
  8. Jan 25, 2012 #7

    HallsofIvy

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    But "Rhapsody" sounds so much better!
     
  9. Jan 25, 2012 #8

    Mark44

    Staff: Mentor

    Well, there's that.
     
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