The sum of all the real roots of the equation |x−2|2+|x−2|−2=0 is

The given equation is |x−2|2+|x−2|−2=0There are two cases: Case I: If x≥2, then (x−2)2+x−2−2=0             ⇒x2−3x=0⇒x(x−3)=0⇒x=0,3Here, 0 is not possible. x=3Case II : If x <2, then             ⇒(x−2)2−x+2−2=0⇒x2−5x+4=0⇒(x−1)(x−4)=0x=1,4Here, 4 is not possible. x=1∴The sum of roots =1+3 = 4