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Math Help - Roots Question..

  1. #1
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    Roots Question..

    Root (4+ root(4 - root(4+ root(4-..... Infinity

    Plz solve this..

    To find SUm
    Last edited by umangarora; September 3rd 2010 at 01:03 AM.
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  2. #2
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    You haven't posted the link properly.
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  3. #3
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    Now its k.. PLZ HELP
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  4. #4
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    Hello, umangarora!

    Evaluate: . \sqrt{4 + \sqrt{4+ \sqrt{4 + \sqrt{4 + \hdots}}}}

    \text{We have: }\;x \;=\;\sqrt{4 + \underbrace{\sqrt{4 + \sqrt{4 + \sqrt{4 + \hdots}}}}_{\text{This is }x} }

    Hence: . x \:=\:\sqrt{4+x} \quad\Rightarrow\quad x^2 \:=\:4 + x \quad\Rightarrow\quad x^2 - x - 4 \:=\:0

    Quadratic Formula: . x \;=\;\dfrac{1\pm\sqrt{17}}{2}

    And the positive root is: . x \;=\;\dfrac{1+\sqrt{17}}{2}
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  5. #5
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    Umm its alternative + - signs.. root 4 + root 4 -..
    any way got the idea,! THANK YOU
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