Question 2
Let $x$, $y$, $z$ be positive numbers such that
$$
\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 1.
$$
Show that
$$
\sqrt{x + y z} + \sqrt{y + z x} + \sqrt{z + x y} \geq \sqrt{x y z} + \sqrt{x} + \sqrt{y} + \sqrt{z}.
$$
$$
\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 1.
$$
Show that
$$
\sqrt{x + y z} + \sqrt{y + z x} + \sqrt{z + x y} \geq \sqrt{x y z} + \sqrt{x} + \sqrt{y} + \sqrt{z}.
$$