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==
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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]])
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==Video Solution (HOW TO THINK CREATIVELY!!!)==
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https://youtu.be/fOakoTBF_cE
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~Education, the Study of Everything
  
 
==See Also==
 
==See Also==

Latest revision as of 14:42, 9 June 2023

Problem

The sum of two nonzero real numbers is 4 times their product. What is the sum of the reciprocals of the two numbers?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 4\qquad\textbf{(D)}\ 8\qquad\textbf{(E)}\ 12$

Solution

Let $x, y$ be our two numbers. Then $x+y = 4xy$. Thus,

$\frac{1}{x} + \frac{1}{y} = \frac{x+y}{xy} = 4$.

$\boxed{ \textbf{C}}$.

Solution 2

We can let $x=y.$ Then, we have that $2x=4x^2$ making $x=\tfrac{1}{2}.$ The answer is $\dfrac{2}{x}=4=\boxed{ \textbf{C}}.$ ~ Solasky (talk)

Video Solution (HOW TO THINK CREATIVELY!!!)

https://youtu.be/fOakoTBF_cE

~Education, the Study of Everything

See Also

2017 AMC 10A (ProblemsAnswer KeyResources)
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 (ProblemsAnswer KeyResources)
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

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