Problem:
What is the sum of all real numbers for which
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Split the equation into two cases, where the value inside the absolute value is positive and nonpositive.
Case 1:
The equation yields , which is equal to . Therefore, the two values for the positive case are and .
Case 2:
Similarly, taking the nonpositive case for the value inside the absolute value notation yields . Factoring and simplifying gives , so the only value for this case is .
Summing all the values results in
The problems on this page are the property of the MAA's American Mathematics Competitions