Problem:
Positive real numbers and satisfy and . What is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The second equation can be written as the difference of squares: . Then . Because and are positive, the only solution to this equation is . Substituting into the first equation gives , so and . The requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions