Repeating Radicals

Algebra Level 4

1+1111+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.

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