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
(rigor needed)
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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