1983 AIME Problems/Problem 9
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 ).
Find the minimum value of for .
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 ).
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