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Math Help - Find the Real Solutions

  1. #1
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    Find the Real Solutions

    I need to find the real solutions to a simple equation:

    \sqrt{x+5}=x

    x+5=x^2

    x^2-x-5=0

    x=\frac{1\pm \sqrt{21}}{2}

    It seems that there should be two real solutions to the equation. However, I am told that the equation has only 1 real solution.
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  2. #2
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    Quote Originally Posted by adkinsjr View Post
    I need to find the real solutions to a simple equation:

    \sqrt{x+5}=x

    x+5=x^2

    x^2-x-5=0

    x=\frac{1\pm \sqrt{21}}{2}

    It seems that there should be two real solutions to the equation. However, I am told that the equation has only 1 real solution.
    From the first equation you know that \sqrt{x+5} is a positive real number. Therefore x must be a positive real number.
    But your last equation has also a negative number which can't be a solution of the original equation.
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  3. #3
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    Only one solution

    There is only one real solution: 2.79129.

    In your first step, you squared both sides. You forgot that it is "plus or minus" though, when you do that. Make sense?


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