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Math Help - Quadratic question

  1. #1
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    Quadratic question

    Please refer to the attached question.
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  2. #2
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    Quote Originally Posted by yeoky View Post
    Find the value of 1 + \frac{3}{1 + \frac{3}{1 + \frac{3}{1 + ... }}}

    Let the value be x. Then you have to solve x = 1 + \frac{3}{x}.
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  3. #3
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    Hello, yeoky!

    \text{Find the value of: }\;x \;=\;1 + \frac{3}{1 + \dfrac{3}{1 + \dfrac{3}{1 + \hdots}}}

    \text{We have: }\;x \;=\;1 + \frac{3}{\begin{Bmatrix}1 + \dfrac{3}{1 + \dfrac{3}{1 + \hdots}}\end{Bmatrix}} \;\;\begin{array}{c}\\ \\ \\ \leftarrow\:\text{ This is }x \end{array}

    That is: . x \;=\;1 + \frac{3}{x}

    Multiply by x\!:\;\;x^2 \:=\:x + 3 \quad\Rightarrow\quad x^2 - x - 3 \:=\:0

    Quadratic Formula . x \;=\;\frac{1 \pm\sqrt{13}}{2}


    Since x is positive: . x \;=\;\frac{1 + \sqrt{13}}{2}

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