Question 41
Let $a$, $b$, $c$, $d$ be real numbers with $0 \lt a, b, c, d \lt 1$ and $a + b + c + d = 2$. Show that
$$
\sqrt{(1 - a)(1 - b)(1 - c)(1 - d)} \le \frac{ac + bd}{2}.
$$
Are there infinitely many cases of equality?
$$
\sqrt{(1 - a)(1 - b)(1 - c)(1 - d)} \le \frac{ac + bd}{2}.
$$
Are there infinitely many cases of equality?