Mock AIME 1 2007-2008 Problems/Problem 13
Problem
Let be a polynomial such that and for such that both sides are defined. Find .
Solution
Combining denominators and simplifying, It becomes obvious that , for some constant , matches the definition of the polynomial. To prove that must have this form, note that
Since and divides the right side of the equation, and divides the left side of the equation. Thus divides , so divides .
It is easy to see that is a quadratic, thus as desired.
By the given, . Thus, .
See also
Mock AIME 1 2007-2008 (Problems, Source) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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