2011 AIME I Problems/Problem 9
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Problem
Suppose is in the interval
and
. Find
.
Solution
We can rewrite the given expression as
Square both sides and divide by
to get
Rewrite
as
Testing values using the rational root theorem gives
as a root,
does fall in the first quadrant so it satisfies the interval. Thus
Using the Pythagorean Identity gives us
. Then we use the definition of
to compute our final answer.
.
See also
2011 AIME I (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 |
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