1988 AIME Problems/Problem 4
Contents
[hide]Problem
Suppose that for . Suppose further that What is the smallest possible value of ?
Solution
Solution 1
Since then
So . We now just need to find an example where : suppose and ; then on the left hand side we have . On the right hand side, we have , and so the equation can hold for .
Solution 2
Let and , Then the smallest value of because , and therefore .
See also
1988 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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