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SMO 2016 Open Round 1 Question 8

SMO · SMO 2016 Open Round 1

Question 8

Find the number of integer solutions to the equation $$\frac{\sqrt x}{\sqrt{2018-x}+\sqrt x}+\frac{\sqrt x}{\sqrt x-\sqrt{2018-x}}-\frac{1009}{x-1009}=1.$$