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SMO 2022 Senior Round 1 Question 9

SMO · SMO 2022 Senior Round 1

Question 9

Suppose $$y=\frac{\tan^2x-\tan x+\sqrt{33}}{\tan^2x+\tan x+1},$$ where $-90^\circ\lt x\lt 90^\circ$. Find the maximum possible value of $\sqrt{33}(y-5)$.