1. ## Radical equation..!??

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

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

2. 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 $x=4^{-n}$