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Algebra Difficulty 4.7 AIME Find the answer

How many roots does arctan⁡x=x2−1.6\arctan x=x^{2}-1.6 have, where the arctan function is defined in the range −pi2<arctan⁡x<pi2-\frac{p i}{2}<\arctan x<\frac{p i}{2} ?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

2.

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