Question 13
Let $x$, $y$, $z$ be real numbers such that $x \ge y \ge z \ge 0$ and $2x + y + 2z = 5$. Prove that
$$
5 \le x^2 + z^2 + xy + yz + zx \le \frac{25}{4}.
$$
When does the equality case hold?
$$
5 \le x^2 + z^2 + xy + yz + zx \le \frac{25}{4}.
$$
When does the equality case hold?