The sum of all the roots of the equation (x-1)^2-5|x-1|+6=0, is :

Question

The sum of all the roots of the equation $(x-1)^2-5|x-1|+6=0$, is :

Accepted Answer

$\begin{gathered} |x-1|2-5|x-1|+6=0 \ |x-1|=t \ {t}^{2}-5+6=0 \ (t-3)(t-2)=0 \ t=2,3 \ |x-1|=2|x-1|=3 \ x-1=\pm 2x-1=\pm 3 \ \Rightarrow x=3,-1,4,-2 \ \Rightarrow =3-1+4-2 \ \, =4 \end{gathered}$

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