Difference between revisions of "1983 AIME Problems/Problem 9"
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Therefore, the minimum value is <math>12</math> (when <math>x\sin{x}=\frac23</math>). | Therefore, the minimum value is <math>12</math> (when <math>x\sin{x}=\frac23</math>). | ||
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== See also == | == See also == | ||
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[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] | ||
[[Category:Intermediate Trigonometry Problems]] | [[Category:Intermediate Trigonometry Problems]] |
Revision as of 20:41, 20 December 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 ).
See also
1983 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |