What is the sum of all the real roots of the equation: |x−2|^2+|x−2|−2=0

Question

Solve for the parameter a for which the sum of all of the real valued roots to the equation sin(√(ax – x2)) = 0 is exactly equal to 100.

Answer 1

Answer: 3+1 = 4.
Given eqn.:
|x−2|2+|x−2|−2=0|x−2|2+|x−2|−2=0
Let , |x−2|=y|x−2|=y
⇒ y2+y−2=0⇒y2+y−2=0
⇒y=−2or1⇒y=−2or1
⇒|x−2|=−2,or1⇒|x−2|=−2,or1
Since the roots are real, |x−2|=1|x−2|=1
⇒x=1or3⇒x=1or3
sum of the roots=3+1=4