Problem:
Ted mistakenly wrote as . What is the sum of all real numbers for which these two expressions have the same value?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Notice that , so the first expression is
and the second expression is
These two expressions have the same value if and only if . Multiplying both sides of this equation by , rearranging terms, and factoring gives . The solutions of this equation are and . The requested sum of possible values for is .
The problems on this page are the property of the MAA's American Mathematics Competitions