CMO 1998 Problem 2

Find all real numbers $x$ such that: $x = \sqrt{ x - \frac{1}{x} } + \sqrt{ 1 - \frac{1}{x} }$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.