RU-ALLRUSSIAN 1985 Problem 20

$\mathrm{x}$ is a real number. Define $\mathrm{x}_0 = 1 + \sqrt{(1 + \mathrm{x})}$ , $\mathrm{x}_1 = 2 + \mathrm{x} / \mathrm{x}_0$ , $\mathrm{x}_2 = 2 + \mathrm{x} / \mathrm{x}_1$ , ..., $\mathrm{x}_{1985} = 2 + \mathrm{x} / \mathrm{x}_{1984}$ . Find all solutions to $\mathrm{x}_{1985} = \mathrm{x}$ .