Difference between revisions of "2025 AIME I Problems/Problem 8"
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| − | + | ==Problem== | |
| + | Let <math>k</math> be a real number such that the system | ||
| + | has exactly one complex solution <math>z</math>. The sum of all possible values of <math>k</math> can be written as <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m + n</math>. Here <math>i = \sqrt{-1}</math>. | ||
| + | ==Solution 1== | ||
Revision as of 18:27, 13 February 2025
Problem
Let 
be a real number such that the system
has exactly one complex solution 
. The sum of all possible values of can be written as 
, where 
and 
are relatively prime positive integers. Find 
. Here 
.
