Difference between revisions of "2002 AMC 10P Problems/Problem 12"
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== Solution 1== | == Solution 1== | ||
| + | We can solve this problem with a case by case check of <math>\text{I., II., III.,}</math> and <math>\text{IV.}</math> Since <math>f_n=x^n,</math> <math>f_{2002}(a)=a^{2002}, all cases must equal </math>a^{2002}.<math> | ||
| + | </math>\text{I. } (f_{11}(a)f_{13}(a))^{14}<math> | ||
| + | </math>\begin{align*} | ||
| + | (f_{11}(a)f_{13}(a))^{14} \\ | ||
| + | &= (a^{11}a^{13})^{14} | ||
| + | &= (a^{24})^14 | ||
| + | &= a^{336} | ||
| + | &\neq a^{2002}$ | ||
== See also == | == See also == | ||
{{AMC10 box|year=2002|ab=P|num-b=11|num-a=13}} | {{AMC10 box|year=2002|ab=P|num-b=11|num-a=13}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 04:37, 15 July 2024
Problem 12
For 
and 
consider
Which of these equal 
Solution 1
We can solve this problem with a case by case check of 
and 
Since 
a^{2002}.$$ (Error compiling LaTeX. Unknown error_msg)\text{I. } (f_{11}(a)f_{13}(a))^{14}$$ (Error compiling LaTeX. Unknown error_msg)\begin{align*}
(f_{11}(a)f_{13}(a))^{14} \\
&= (a^{11}a^{13})^{14}
&= (a^{24})^14
&= a^{336}
&\neq a^{2002}$
See also
| 2002 AMC 10P (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 | ||
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