Mock AIME 2 Pre 2005 Problems/Problem 11
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, , 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:
$\alpha\beta + \beta\gamma + \gamma\alpha & = -50$ (Error compiling LaTeX. Unknown error_msg)
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |