Mock AIME 3 Pre 2005 Problems/Problem 4
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Problem
and are complex numbers such that
Compute .
Solution
We let (the elementary symmetric sums). Then, we can rewrite the above equations as from where it follows that . The third equation can be factored as from where it follows that . Thus, applying Vieta's formulas backwards, and are the roots of the polynomial Let (the power sums). Then from , we have the recursion . It follows that .
See Also
Mock AIME 3 Pre 2005 (Problems, Source) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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