Mock AIME 2 Pre 2005 Problems/Problem 11
, , and are the roots of . Let The value of can be written as where and are relatively prime positive integers. Determine the value of .
Solution
We know that are the roots of . By Vieta's formulas, we have:
Now, by tangent addition formulas, we have . Substituting Vieta's formulas, we obtain . Therefore, our answer is and we are done.
See also
Mock AIME 2 Pre 2005 (Problems, Source) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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