NL-NWO 1973 Problem 4

We have an infinite sequence of real numbers $x_0,x_1, x_2, ...$ such that $x_{n+1} = \sqrt{x_n -\frac14}$ holds for all natural $n$ and moreover $x_0 \in \frac12$ . (a) Prove that for every natural $n$ holds: $x_n > \frac12$ (b) Prove that $\lim_{n \to \infty} x_n$ exists. Calculate this limit.