MathNet 2026 — Part 06 Question 63

Let $a$, $b$, $c$, $d$ be real numbers. Show there is a pair $(x, y)$ of real numbers such that $|x| \le 1$, $|y| \le 1$ and $|a + bx + cy + dxy - \frac{3}{1 + x^2 + y^2}| \ge 1$.