Difference between revisions of "1983 AIME Problems/Problem 9"
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* [[1983 AIME Problems|Back to Exam]] | * [[1983 AIME Problems|Back to Exam]] | ||
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== See also == | == See also == |
Revision as of 20:53, 1 February 2007
Problem
Find the minimum value of for .
Solution
Let .
We can rewrite the expression as .
Since and because , we have .
So we can apply AM-GM:
The equality holds when
Therefore, the minimum value is (when ).
1983 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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