Difference between revisions of "2017 AMC 12A Problems/Problem 2"
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<math>\boxed{ \textbf{C}}</math>. | <math>\boxed{ \textbf{C}}</math>. | ||
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+ | ==Solution 2== | ||
+ | We can let <math>x=y.</math> Then, we have that <math>2x=4x^2</math> making <math>x=\tfrac{1}{2}.</math> The answer is <math>\dfrac{2}{x}=4=\boxed{ \textbf{C}}.</math> ~ [[User:Solasky|Solasky]] ([[User talk:Solasky|talk]]) | ||
==See Also== | ==See Also== |
Revision as of 16:35, 17 October 2021
Contents
Problem
The sum of two nonzero real numbers is 4 times their product. What is the sum of the reciprocals of the two numbers?
Solution
Let be our two numbers. Then
. Thus,
.
.
Solution 2
We can let Then, we have that
making
The answer is
~ Solasky (talk)
See Also
2017 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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 |
2017 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 1 |
Followed by Problem 3 |
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.