Difference between revisions of "Mock AIME II 2012 Problems/Problem 11"
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Revision as of 03:17, 5 April 2012
Problem
There exist real values of and such that , , and for some value of . Let be the sum of all possible values of . Find .
Solution
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.)