Question 58
Prove that every positive real number $x$ satisfies
$$
\sqrt{x^{2}-x+\frac{1}{2}} \geq \frac{1}{x+\frac{1}{x}}
$$
$$
\sqrt{x^{2}-x+\frac{1}{2}} \geq \frac{1}{x+\frac{1}{x}}
$$
MathNet 2026 — Part 10 Question 58
Math Olympiad Vault · MathNet 2026 — Part 10