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Math Help - [SOLVED] Help on Quadratic Equation

  1. #1
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    [SOLVED] Help on Quadratic Equation

    Hello, I need some help with this problem.

    The problem is:

     Ln(x) + Ln(x-1) = 1

    Heres what I got
    ----------------

    Ln(x) + Ln(x-1) = 1]

    Ln(x^2 - x) = 1

    x^2 - x = e^1

    x^2 - x - e = 0

    Now I use the quadratic equation to get

    \frac{x \pm \sqrt{x^2 - 4(x^2)(-e)}}{2x^2}

    The answer is supposed to be :
    <br />
\frac{(1 \pm \sqrt{1 + 4e})}{2}

    I'm having some difficulty seeing how they got that answer.

    Did I do something incorrectly? Or am I simplifying wrong?

    Thank you
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  2. #2
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    Quote Originally Posted by sleels View Post
    Hello, I need some help with this problem.

    The problem is:

     Ln(x) + Ln(x-1) = 1

    Heres what I got
    ----------------

    Ln(x) + Ln(x-1) = 1]

    Ln(x^2 - x) = 1

    x^2 - x = e^1

    x^2 - x - e = 0

    Now I use the quadratic equation to get

    \frac{x \pm \sqrt{x^2 - 4(x^2)(-e)}}{2x^2}

    The answer is supposed to be :
    <br />
\frac{(1 \pm \sqrt{1 + 4e})}{2}

    I'm having some difficulty seeing how they got that answer.

    Did I do something incorrectly? Or am I simplifying wrong?

    Thank you
    x^2 - x - e = 0

    a = 1, b = -1, c = -e. These are what you're meant to substitute into the quadratic formula.
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  3. #3
    MHF Contributor

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    Quote Originally Posted by sleels View Post
    Hello, I need some help with this problem.

    The problem is:

     Ln(x) + Ln(x-1) = 1

    Heres what I got
    ----------------

    Ln(x) + Ln(x-1) = 1]

    Ln(x^2 - x) = 1

    x^2 - x = e^1

    x^2 - x - e = 0

    Now I use the quadratic equation to get

    \frac{x \pm \sqrt{x^2 - 4(x^2)(-e)}}{2x^2}

    The answer is supposed to be :
    <br />
\frac{(1 \pm \sqrt{1 + 4e})}{2}

    I'm having some difficulty seeing how they got that answer.

    Did I do something incorrectly? Or am I simplifying wrong?

    Thank you
    You don't put the "x" inside the solution! The "a", "b", and "c" in the quadratic formula, \frac{-b\pm\sqrt{b^2- 4ac}}{2a} are the numbers multiplying x and x^2. In x^2- x- e= 0, a= 1, b= -1, and c= -e.
    Last edited by mr fantastic; September 3rd 2009 at 04:37 AM. Reason: Fixed a latex tag
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  4. #4
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    doh! I knew it was something stupid.

    Thanks a bunch
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