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Find all real numbers

Source: IMOC 2021 A1

August 11, 2021
algebraequation

Problem Statement

Find all real numbers x that satisfiesx−1x+1−1x−1x−1x+1−1x+1−1x−1x+1−1x=x.\sqrt{\sqrt{x-\frac{1}{x}}+\sqrt{1-\frac{1}{x}}-\frac{1}{\sqrt{x-\frac{1}{x}}+\sqrt{1-\frac{1}{x}}}}+\sqrt{1-\frac{1}{\sqrt{x-\frac{1}{x}}+\sqrt{1-\frac{1}{x}}}}=x. [url=https://artofproblemsolving.com/community/c6h2645263p22889979]2021 IMOC Problems
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