1983 AIME Problems/Problem 3
Problem
What is the product of the real roots of the equation 
?
Solution
If we expand by squaring, we get a quartic polynomial, which obviously isn't very helpful.
Instead, we substitute 
for 
and our equation becomes 
.
Now we can square; solving for , we get 
or 
. The second solution gives us non-real roots, so we'll will go with the first. Substituting back in for ,
. The product of our roots is therefore 20.
