2002 AIME I Problems/Problem 6
Problem
The solutions to the system of equations
are and . Find .
Solution
Let and let .
From the first equation: .
Plugging this into the second equation yields and thus, .
So, .
And .
Thus, .
One may simplify the work by applying Vieta's formulas to directly find that .
See also
2002 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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.