Question

The solutions of the equation $(3|x|-3{)}^2=|x|+7$ which belongs to the domain of definition of the function $\sqrt{\left\{x(x-3)\right\}}$ are given by:

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Domain of definition of the function

$y=$ $\sqrt{\left[x\right(x-3\left)\right]})$ is $x(x-3)\ge 0$

i.e., $x\le 0$ or $x\ge 3$ .........(1)

Given equation can be re-written as

$9|x{|}^2-19|x|+2=0$

$i.e.,(9|x|-1)(|x|-2)=0$

$i.e.,|x|=2or|x|=\frac{1}{9}$

$\therefore$ Solution of the given equation are

$\pm 2,\pm \frac{1}{9}$ .............(2)

In the domain (1), the required solutions are $-2,-\frac{1}{9}$.