Question 19
Solve the equation
$$
\sqrt{x+\sqrt{4 x+\sqrt{16 x+\sqrt{\ldots+\sqrt{4^{2008} x+3}}}}}-\sqrt{x}=1
$$
Express your answer as a reduced fraction with the numerator and denominator written in their prime factorization.
$$
\sqrt{x+\sqrt{4 x+\sqrt{16 x+\sqrt{\ldots+\sqrt{4^{2008} x+3}}}}}-\sqrt{x}=1
$$
Express your answer as a reduced fraction with the numerator and denominator written in their prime factorization.