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Thread: Radical equation..!??

  1. #1
    Super Member dhiab's Avatar
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    Radical equation..!??

    $\displaystyle n \in {\rm N}$
    Solve in R the equation :

    $\displaystyle \sqrt {x + \sqrt {4x + \sqrt {16x + \sqrt {4^n x + 3} } } } - \sqrt x = 1$
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  2. #2
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    Quote Originally Posted by dhiab View Post
    $\displaystyle n \in {\rm N}$
    Solve in R the equation :

    $\displaystyle \sqrt {x + \sqrt {4x + \sqrt {16x + \sqrt {4^n x + 3} } } } - \sqrt x = 1$
    Interesting problem. Assume the problem to be:

    $\displaystyle \sqrt {x + \sqrt {4x + \sqrt {16x + \sqrt{ 64x+... +\sqrt {4^n x + 3} } } } } - \sqrt x = 1$

    - Put $\displaystyle \sqrt x $ on the RHS, square both sides, cancel out the terms $\displaystyle 4^k x, k=0, 1, 2, ..., n $, would finally get $\displaystyle x=4^{-n} $
    Last edited by mr fantastic; Sep 18th 2009 at 08:19 AM. Reason: Restored original reply
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