Maths Olympiad Prep

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Algebra Difficulty 4.0 AMC 10/12 Find the answer United States

Problem:

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 −π2<arctan⁡x<π2-\frac{\pi}{2} < \arctan x < \frac{\pi}{2}?

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

Solution

Solution:

2 .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.