Question 93
Let $a$ and $x_{1}$ be two positive real numbers. Show that the sequence $\left(x_{n}\right)_{n=1}^{\infty}$ defined by the relation
$$
x_{n+1}=\frac{1}{2}\left(x_{n}+\frac{a}{x_{n}}\right), \forall n \geq 1
$$
has a limit, and determine this limit.
$$
x_{n+1}=\frac{1}{2}\left(x_{n}+\frac{a}{x_{n}}\right), \forall n \geq 1
$$
has a limit, and determine this limit.