Suppose that \( f : (2, \infty) \to (-2, 2) \) is a continuous function and there exists a positive constant \( m \) such that \( | 1 + xf(x) + (f(x))^2 | \leq m \) for any \( x > 2 \). Prove that, for any \( x > 2 \),
\[
\left| f(x) – \frac{\sqrt{x^2 -4}-x}{2} \right| \leq 6 \sqrt{m}.
\]

The best solution was submitted by Huy Tùng Nguyễn (2016학번). Congratulations!

Here is his solution of problem 2017-05.

Alternative solutions were submitted by 위성군 (수리과학과 2015학번, +3), 조태혁 (수리과학과 2014학번, +3), 최인혁 (물리학과 2015학번, +3), 장기정 (수리과학과 2014학번, +3), 최대범 (수리과학과 2016학번, +3), 오동우 (수리과학과 2015학번, +3), 이본우 (2017학번, +3), 김재현 (수리과학과 2016학번, +3), 김태균 (수리과학과 2016학번, +2).