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 
.
