Problem:
Two different positive numbers and each differ from their reciprocals by 1 . What is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
A number differs by one from its reciprocal if and only if or . These equations are equivalent to and . Solving these by the quadratic formula yields the positive solutions
which are reciprocals of each other. The sum of the two numbers is .
The problems on this page are the property of the MAA's American Mathematics Competitions