HMMT February, 2019

Algebra Difficulty 4.6 AIME Prove it United States

Problem:
Find the sum of all real solutions to $x^{2} + \cos x = 2019$ .

Solution

Solution:
The left-hand side is an even function, hence for each $x$ that solves the equation, $-x$ will also be a solution. Pairing the solutions up in this way, we get that the sum must be $0$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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