1991 AIME Problems/Problem 7
Contents
[hide]Problem
Find , where is the sum of the absolute values of all roots of the following equation:
Solution
Let . Then , from which we realize that . This is because if we expand the entire expression, we will get a fraction of the form on the right hand side, which makes the equation simplify to a quadratic. As this quadratic will have two roots, they must be the same roots as the quadratic .
The given finite expansion can then be easily seen to reduce to the quadratic equation . The solutions are . Therefore, . We conclude that .
Solution 2
See also
1991 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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