Difference between revisions of "2017 AMC 10A Problems/Problem 5"
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− | Let the two real numbers be <math>x,y</math>. We are given that | + | Let the two real numbers be <math>x,y</math>. We are given that <math>x+y=4xy,</math> and dividing both sides by <math>xy</math>, <math>\frac{x}{xy}+\frac{y}{xy}=4.</math> |
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− | and dividing both sides by <math>xy</math>, | ||
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<cmath>\frac{1}{y}+\frac{1}{x}=\boxed{\textbf{(C) } 4}.</cmath> | <cmath>\frac{1}{y}+\frac{1}{x}=\boxed{\textbf{(C) } 4}.</cmath> |
Revision as of 15:15, 9 February 2017
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 the two real numbers be . We are given that and dividing both sides by ,
Note: we can easily verify that this is the correct answer; for example, 1/2 and 1/2 work, and the sum of their reciprocals is 4.
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.