Question 118
Let $x$, $y$, $z$ be real numbers such that:
$$
x^2 + 4y^2 + 9z^2 + 20 = 4x + 12y + 24z.
$$
Prove that $x \in [-1, 5]$, $y \in [0, 3]$ and $z \in \left[\frac{1}{3}, \frac{7}{3}\right]$.
$$
x^2 + 4y^2 + 9z^2 + 20 = 4x + 12y + 24z.
$$
Prove that $x \in [-1, 5]$, $y \in [0, 3]$ and $z \in \left[\frac{1}{3}, \frac{7}{3}\right]$.