Difference between revisions of "2016 AMC 10B Problems/Problem 3"
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Latest revision as of 16:55, 18 October 2025
Contents
Problem
Let 
. What is the value of 
?
Solution 1
Substituting carefully, 
becomes 
which is 
.
Solution 2
Solution by e_power_pi_times_i
Substitute 
into the equation. Now, it is 
. Since 
, it is a positive number, so 
. Now the equation is 
. This further simplifies to 
, so the answer is 
Video Solution (CREATIVE THINKING)
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Video Solution
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See Also
| 2016 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
