Radical equation..!??

**dhiab** · September 5th 2009, 03:57 AM

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

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

**luobo** · September 5th 2009, 05:25 AM

Originally Posted by dhiab

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

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

Interesting problem. Assume the problem to be:

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

- Put $\sqrt x$ on the RHS, square both sides, cancel out the terms $4^k x, k=0, 1, 2, ..., n$ , would finally get $x=4^{-n}$

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