2018 UMO Problems/Problem 2: Difference between revisions
Bigbrain123 (talk | contribs) Wrote a solution and posted the problem. |
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== Solution 1 == | == Solution 1 == | ||
Plugging in <math>x = 0</math>, we find that <math>abc = 1. Using AM-GM, we have that < | Plugging in <math>x = 0</math>, we find that <math>abc = 1</math>. Using AM-GM, we have that <math>a+b+c \leq 3 \sqrt[3]{abc} = \fbox{3}</math> | ||
~bigbrain123 | |||
Latest revision as of 22:49, 15 July 2023
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 
. Using AM-GM, we have that ![$a+b+c \leq 3 \sqrt[3]{abc} = \fbox{3}$](http://latex.artofproblemsolving.com/5/1/c/51cf21c0f63d719af9d5468f4b85dca6799296ff.png)
~bigbrain123
