2005 AIME I Problems/Problem 8
Revision as of 19:50, 2 January 2022 by Fuzimiao2013 (talk | contribs) (Changed frac mn to m/n since apparently that was how it was written on the actual test)
Problem
The equation has three real roots. Given that their sum is where and are relatively prime positive integers, find
Solution
Let . Then our equation reads or . Thus, if this equation has roots and , by Vieta's formulas we have . Let the corresponding values of be and . Then the previous statement says that so taking a logarithm of that gives and . Thus the answer is .
See also
2005 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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