2012 AIME II Problems/Problem 8
Problem 8
The complex numbers and satisfy the system Find the smallest possible value of .
Solution
Multiplying the two equations together gives us and multiplying by then gives us a quadratic in : Using the quadratic formula, we find the two possible values of to be = The smallest possible value of is then obviously
See also
2012 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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