Question

The number of elements in the set $\{x\in R:(|x|-3)|x+4|=6\}$ is equal to

• A. $2$
• B. $1$
• C. $3$
• D. $4$

Answer 1

The correct option is A $2$

Case$-1:x\le -4$
$(-x-3)(-x-4)=6\Rightarrow (x+3)(x+4)=6\Rightarrow x^2+7x+6=0\Rightarrow x=-1\text{or}-6\text{but}x\le -4x=-6\text{Case}-2:x\in (-4,0)(-x-3)(x+4)=6\Rightarrow -x^2-7x-12-6\Rightarrow x^2+7x+18=0D<0\text{No solution}\text{Case}-3:x\ge 0(x-3)(x+4)=6\Rightarrow x^2+x-12-6=0\Rightarrow x^2+x-18=0\Rightarrow x=\frac{-1\pm \sqrt{1+72}}{2}$
$\therefore x=\frac{\sqrt{73}-1}{2}$ only
Hence $2$ elements only