Question 36
Let $x$, $y$ and $z$ be positive real numbers with $x + y + z = 3$. Prove that at least one of the three numbers
$$
x(x + y - z), \quad y(y + z - x) \quad \text{or} \quad z(z + x - y)
$$
is less or equal $1$.
$$
x(x + y - z), \quad y(y + z - x) \quad \text{or} \quad z(z + x - y)
$$
is less or equal $1$.