Mock AIME II 2012 Problems/Problem 11
There exist real values of and such that , , and for some value of . Let be the sum of all possible values of . Find .
First, if , then . We now assume that . Now, note that . Also, we have .
Next, . But we know , so .
Since the only possible values of are and , our final answer is .
(It is easy to check that there exists satisfying the equations.)