Question

Value(s) of $x$ for $\frac{|x^2-2|x|+1|}{|x|+1}=2$ is/are

• A. $(\pm 2+\sqrt{5})$
• B. $\pm \sqrt{5}$
• C. $\pm (2\pm \sqrt{5})$
• D. $\pm 2$

Answer 1

The correct option is A $(\pm 2+\sqrt{5})$

$\frac{|x^2-2|x|+1|}{|x|+1}=2$
$\Rightarrow (|x|-1{)}^2=2(|x|+1),x\in R$
$\Rightarrow (|x|-1{)}^2=2|x|+2$
$\Rightarrow |x{|}^2-2|x|+1-2|x|-2=0\Rightarrow |x{|}^2-4|x|-1=0\Rightarrow |x|=2\pm \sqrt{5}$
But $|x|=2-\sqrt{5}<0$
$\therefore |x|=2+\sqrt{5}\Rightarrow x=\pm (2+\sqrt{5})$