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Math Help - Solve for X - square root infinite

  1. #1
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    Solve for X - square root infinite

    Solve for x:

    x = \sqrt{3+\sqrt{3+\sqrt{3+...}}}


    I have been stuck on this problem, was hoping for some help. Really confused about the square root under the square root and so on to infinity. Not sure where to begin hoping to be showed steps that get me to an answer. Thanks
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  2. #2
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    Quote Originally Posted by kelly1183 View Post
    Solve for x:

    x = \sqrt{3+\sqrt{3+\sqrt{3+...}}}


    I have been stuck on this problem, was hoping for some help. Really confused about the square root under the square root and so on to infinity. Not sure where to begin hoping to be showed steps that get me to an answer. Thanks
    Hi

    You can see that

    x^2 = 3+\sqrt{3+\sqrt{3+...}}

    x^2 - 3 = \sqrt{3+\sqrt{3+...}}

    x^2 - 3 = x

    This is a quadratic which has only one positive root
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