Question

The solution(s) of the equation $(3|x|-3{)}^2=|x|+7$ which belong to the domain of $\sqrt{x(x-3)}$ is/are

• A. $2$
• B. $-2$
• C. $\frac{1}{9}$
• D. $-\frac{1}{9}$

Answer 1

Answer: (B), (D)

The correct options are
B $-2$
D $-\frac{1}{9}$

$\sqrt{x(x-3)}$
For the square root to be defined,
$x(x-3)\ge 0\Rightarrow x\in (-\infty ,0]\cup [3,\infty )\cdots \left(1\right)$
Now, given quadratic equation
$(3|x|-3{)}^2=|x|+7\Rightarrow 9(|x{|}^2-2|x|+1)=|x|+7\Rightarrow 9|x{|}^2-19|x|+2=0\Rightarrow (|x|-2\left)\right(9|x|-1)=0\Rightarrow |x|=2,\frac{1}{9}\Rightarrow x=\pm 2,\pm \frac{1}{9}$
From equation $\left(1\right)$,
$x=-2,-\frac{1}{9}$