Problem:
Suppose that x and y are nonzero real numbers such that
xβ3y3x+yβ=β2
What is the value of
3xβyx+3yβ?
Answer Choices:
A. β3
B. β1
C. 1
D. 2
E. 3
Solution:
The given equation implies that 3x+y=β2(xβ3y), which is equivalent to x=y. Therefore
3xβyx+3yβ=2y4yβ=(D)2β
The problems on this page are the property of the MAA's American Mathematics Competitions