$\displaystyle n \in {\rm N}$
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} $