Question 98
The positive real numbers $x$, $y$ and $z$ satisfy the relation $x + y + z \geq 1$. Prove the inequality
$$
\frac{x \sqrt{x}}{y + z} + \frac{y \sqrt{y}}{x + z} + \frac{z \sqrt{z}}{x + y} \geq \frac{\sqrt{3}}{2}
$$
$$
\frac{x \sqrt{x}}{y + z} + \frac{y \sqrt{y}}{x + z} + \frac{z \sqrt{z}}{x + y} \geq \frac{\sqrt{3}}{2}
$$