2005 AIME I Problems/Problem 8
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.