Northeastern WOOTers Mock AIME I Problems/Problem 5
Problem 5
Let ,
, and
be real numbers. Given that
, the maximum value of
can be represented
, where
and
are positive integers, where
and
are relatively prime. Find
.
Solution
By the Cauchy-Schwarz Inequality,
It follows that
. Since this is attainable when
, the answer is
.