2015 AIME II Problems/Problem 14
Problem
Let and
be real numbers satisfying
and
. Evaluate
.
Solution
The expression we want to find is .
Factor the given equations as and
, respectively. Dividing the latter by the former equation yields
. Adding 3 to both sides and simplifying yields
. Solving for
and substituting this expression into the first equation yields
. Solving for
, we find that
, so
. Substituting this into the second equation and solving for
yields
. So, the expression to evaluate is equal to
.