Difference between revisions of "2002 AMC 12P Problems/Problem 10"
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== Problem == | == Problem == | ||
Let <math>f_n (x) = \text{sin}^n x + \text{cos}^n x.</math> For how many <math>x</math> in <math>[0,\pi]</math> is it true that | Let <math>f_n (x) = \text{sin}^n x + \text{cos}^n x.</math> For how many <math>x</math> in <math>[0,\pi]</math> is it true that | ||
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+ | <cmath>6f_{4}(x)-4f_{6}(x)=2f_{2}(x)?</cmath> | ||
<math> | <math> |
Revision as of 00:09, 31 December 2023
Problem
Let For how many in is it true that
Solution
If , then . Since , must be to some factor of 6. Thus, there are four (3, 9, 27, 729) possible values of .
See also
2002 AMC 12P (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
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 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.