Difference between revisions of "1983 AIME Problems/Problem 2"
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* [[1983 AIME Problems|Back to Exam]] | * [[1983 AIME Problems|Back to Exam]] | ||
[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] | ||
Revision as of 22:45, 23 July 2006
Problem
Let 
, where 
. Determine the minimum value taken by 
by 
in the interval 
.
Solution
It is best to get rid of the absolute value first.
Under the given circumstances, we notice that 
, 
, and 
.
Adding these together, we find that the sum is equal to 
, of which the minimum value is attained when 
.
The answer is thus 
.
