2018 UMO Problems/Problem 2
Revision as of 17:05, 31 July 2021 by Bigbrain123 (talk | contribs) (Wrote a solution and posted the problem.)
Problem 2
Let be a cubic polynomial
, where
and
are positive real numbers.
Let Q(x) be the polynomial with
. If
for all
, then
find the minimum possible value of
.
Solution 1
Plugging in , we find that
a+b+c \leq 3 ^3\sqrt{abc} = \fbox{3}$