Question 54
Let $x$, $y$ and $z$ be real numbers such that $0 \le x, y, z \le 1$. Prove that
$$
xyz + (1-x)(1-y)(1-z) \le 1.
$$
When does the equality hold?
$$
xyz + (1-x)(1-y)(1-z) \le 1.
$$
When does the equality hold?
MathNet 2010 — Part 06 Question 54
Math Olympiad Vault · MathNet 2010 — Part 06