Question 24
a. Let $n$ be a positive integer. Prove that
$$
n\sqrt{x-n^2} \le \frac{x}{2}, \text{ for all } x \ge n^2.
$$
b. Determine real numbers $x$, $y$, $z$ satisfying the equation
$$
2\sqrt{x-1} + 4\sqrt{y-4} + 6\sqrt{z-9} = x + y + z.
$$
$$
n\sqrt{x-n^2} \le \frac{x}{2}, \text{ for all } x \ge n^2.
$$
b. Determine real numbers $x$, $y$, $z$ satisfying the equation
$$
2\sqrt{x-1} + 4\sqrt{y-4} + 6\sqrt{z-9} = x + y + z.
$$