Question

Solution of $|x||x+1|=2$ is

• A. $\{-1,1\}$
• B. $\{-2,1\}$
• C. $\{-3,2\}$
• D. $\{-4,-2\}$

Answer 1

The correct option is B $\{-2,1\}$

$|x||x+1|=2$
$\because [|a||b|=|ab|]$
$\Rightarrow |x(x+1)|=2$
$\Rightarrow x^2+x=\pm 2$
$\Rightarrow x^2+x-2=0$ or $x^2+x+2=0$
$\Rightarrow (x-1)(x+2)=0$ or $x=\frac{-1\pm \sqrt{1-4\left(1\right)2}}{2}$
$\Rightarrow x=1,-2$ or
no real value of $x$ $($as $D<0)$
Hence, required solution is $x=\{1,-2\}$