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Math Help - Fixed Points

  1. #1
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    Fixed Points

    Hi,

    I am having trouble working out this. I have got this equation, x^2 -x - 0.5 = 0. Then the answer is 0.5√3, which is +/-0.366. How can you find that value?

    Any help needed.
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by mark090480 View Post
    Hi,

    I am having trouble working out this. I have got this equation, x^2 -x - 0.5 = 0. Then the answer is 0.5√3, which is +/-0.366. How can you find that value?

    Any help needed.
    Quadratic formula is fastest:

    For ax^2+bx+c=0

    x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}

    In your case:

    \frac{1 \pm \sqrt{3}}{2} = \frac{1}{2} \pm \frac{\sqrt3}{2}
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  3. #3
    MHF Contributor

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    What, exactly, is the question? You title this "fixed point" but then just give a quadratic equation. The quadratic equation can, of course, be solved using the quadratic formula as e^(i*pi) said.
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  4. #4
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    The question is about finding the limit using the fixed point rule. You can do that using the quadratic equation, not sure if that is what I should do. The question is this:

    x0 = xn+1 = xn^2 -1/2 (n= 0,1,2...)

    Generated by this function f(x) = x^2 - 1/2 appears to converge to a limit between -0.5 and 0. Assuming that this convergence does occur, find the value of the limit.

    This question came after learning the fixed point rule, which I don't understand. If you have a link or knowledge about that; that would be useful.

    Thanks.
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