2005 AIME I Problems/Problem 8
Problem
The equation has three real roots. Given that their sum is
where
and
are relatively prime positive integers, find
Solution
Let . Then our equation reads
or
. Thus, if this equation has roots
and
, we have
. Let the corresponding values of
be
and
. Then the previous statement says that
so that taking a logarithm gives
and
. Thus the answer is
.