1997 AIME Problems/Problem 14
Problem
Let and be distinct, randomly chosen roots of the equation . Let be the probability that , where and are relatively prime positive integers. Find .
Solution
By De Moivre's Theorem, we find that
Now, let be the root corresponding to , and let be the root corresponding to . The magnitude of is therefore:
We need . The cosine difference identity simplifies that to . Thus, .
See also
1997 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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All AIME Problems and Solutions |