Adopted from the Vermont Math contest

Algebra Level 3

Find the smallest positive real xx such that x2xx=6.\big\lfloor x^2 \big\rfloor-x\lfloor x \rfloor=6. If your answer is in the form ab\frac{a}{b}, where aa and bb are coprime positive integers, submit your answer as a+b.a+b.


Notation: \lfloor \cdot \rfloor denotes the floor function.

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