Question 1
A sequence of positive real numbers $x_0,x_1,x_2,\ldots$ is defined by
$$x_0=b,\qquad x_{n+1}=\sqrt{c-\sqrt{c+x_n}}.$$
Find all values of $c$ such that, for every $b\in(0,c)$, this sequence exists and converges to a limit as $n$ tends to infinity.
$$x_0=b,\qquad x_{n+1}=\sqrt{c-\sqrt{c+x_n}}.$$
Find all values of $c$ such that, for every $b\in(0,c)$, this sequence exists and converges to a limit as $n$ tends to infinity.