Difference between revisions of "2013 AMC 12A Problems/Problem 4"
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<math>\frac{(2^2+1)}{(2^2-1)}=\frac{5}{3}</math>, which is <math>C</math> | <math>\frac{(2^2+1)}{(2^2-1)}=\frac{5}{3}</math>, which is <math>C</math> | ||
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+ | ==Solution 2== | ||
+ | Suppose that <cmath>x=2^{2012}.</cmath> Then the given expression is equal to <cmath>\frac{4x+x}{4x-x}=\frac{5x}{3x}=\boxed{\frac{5}{3}\textbf{(C)}}.</cmath> | ||
+ | |||
+ | ~sugar_rush | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://www.youtube.com/watch?v=2vf843cvVzo?t=545 (solution for #4 starts at 9:05) | ||
+ | |||
+ | ~sugar_rush | ||
== See also == | == See also == |
Latest revision as of 22:13, 23 November 2020
Problem
What is the value of
Solution
We can factor a out of the numerator and denominator to obtain
The cancels, so we get
, which is
Solution 2
Suppose that Then the given expression is equal to
~sugar_rush
Video Solution
https://www.youtube.com/watch?v=2vf843cvVzo?t=545 (solution for #4 starts at 9:05)
~sugar_rush
See also
2013 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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 |
2013 AMC 12A (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 • 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.