Difference between revisions of "2017 AMC 12A Problems/Problem 2"
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| + | Solution 2. Use Simon's Favorite Factoring Trick to find x and y | ||
| + | (4xy)=x+y 4xy-x-y=0 (4x-1)(y-1/4)=1/4 (4x-1)=1/2 x=3/8 (y-1/4)=1/2 y=3/4 add the reciprocals 8/3+4/3=4 | ||
==See Also== | ==See Also== | ||
Revision as of 10:45, 3 April 2020
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. Use Simon's Favorite Factoring Trick to find x and y (4xy)=x+y 4xy-x-y=0 (4x-1)(y-1/4)=1/4 (4x-1)=1/2 x=3/8 (y-1/4)=1/2 y=3/4 add the reciprocals 8/3+4/3=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. 
