Explanation

(d)
Domain of the function $y = \sqrt{x(x - 3)}$ is $x(x - 3) \geq 0$
$\Rightarrow x \leq 0\ or\ x \geq 3$ …(i)
Given equation can be rewritten as
$9|x|^{2} - 19|x| + 2 = 0$
$\Rightarrow \left( 9|x| - 1 \right)\left( |x| - 2 \right) = 0$
$\Rightarrow |x| = 2\ \ or\ \ |x| = \frac{1}{9}$
$\therefore$ Solution of the given equation are $\pm 2,\ \pm \frac{1}{9}.$
In the domain (i) the required solutions are $- 2,\ - \frac{1}{9}$.