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Geometry Level 3

What is the number of solutions of ∣ x ∣ = cos ⁡ ( x ) |x|= \cos(x) ?

2 3 0 1

Aniruddha Bagchi by Aniruddha Bagchi , 20, India

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1 solution

Aniruddha Bagchi
May 19, 2017

Picture the graph of cos x and |x| seperately then merge them. You get two intersections .. so you get 2 solutions.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The solution doesn't quite feel satisfactory. We can "picture the graph of 100 cos ⁡ x 100 \cos x and ∣ x ∣ |x| separately, and it's unclear how many intersections we get when merged.

Thus, there still has to be a reasoning for why there are no further intersections. At the very least, explain why we only care about 0 < x ≤ 1 0 < x \leq 1 , where the cosine function is decreasing and |x| is increasing, so there is at most one solution.

Calvin Lin Staff - 4 years ago

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