Question

The sum of real roots of the equation $|x-2{|}^2+|x-2|-2=0$ is

Answer 1

$|x-2{|}^2+|x-2|-2=0$
$\Rightarrow (|x-2|+2)(|x-2|-1)=0$
$\Rightarrow |x-2|-1=0$
$\Rightarrow x-2=\pm 1$
$\Rightarrow x=1,3$
Therefore, the sum of the roots is $3+1=4$