Algebra-2

To find the extraneous solution of the equation , we need to consider two cases based on the definition of the absolute value and then check the obtained solutions.

Case 1: When , i.e.,

In this case, the the absolute value . So our equation becomes:





However, we assumed at the beginning of this case that

, and does not satisfy this condition. So is a candidate for an extraneous solution at this point.

Case 2: When , i.e.,
In this case, the absolute value