2016 AIME II Problems/Problem 15
For let
and
. Let
be positive real numbers such that
and
. The maximum possible value of
, where
and
are relatively prime positive integers. Find
.
Solution
Replace with
and the second equation becomes
. Conveniently,
so we get
. This is the equality case of Cauchy so
for some constant
. Using
, we find
and thus
. Thus, the desired answer is
.