Question

The sum of all real roots of the equation ${\left(x-2\right|}^2+\left(x-2\right|-2=0$ is

Answer 1

${\left(x-2\right|}^2+\left(x-2\right|-2=0\Rightarrow \left(\left(x-2\right|+2\right)\left(\left(x-2\right|-1\right)=0\left(x-2\right|+2=0\Rightarrow \left(x-2\right|=-2\mathrm{which}\mathrm{is}\mathrm{not}\mathrm{possible}\left(x-2\right|-1=0\Rightarrow \left(x-2\right|=1\Rightarrow x-2=\pm 1\Rightarrow x=3,1\mathrm{Sum}=1+3=4$