2002 AMC 12A Problems/Problem 13
Problem
Two different positive numbers and each differ from their reciprocals by . What is ?
Solution
Each of the numbers and is a solution to .
Hence it is either a solution to , or to . Then it must be a solution either to , or to .
There are in total four such values of , namely .
Out of these, two are positive: and . We can easily check that both of them indeed have the required property, and their sum is .
See Also
2002 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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All AMC 12 Problems and Solutions |