Repeating Radicals

Algebra Level 4

1+11−11+11−⋯\large \sqrt{1 + \dfrac{1}{\sqrt{1 - \dfrac{1}{\sqrt{1 + \dfrac{1}{\sqrt{1 - \cdots}}}}}}}

If the above expression equals x,x, then determine ⌊1000x⌋.\lfloor 1000x \rfloor.

Brian Charlesworth by Brian Charlesworth
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