Problem:
Given that x and y are distinct nonzero real numbers such that x+x2β=y+y2β, what is xy ?
Answer Choices:
A. 41β
B. 21β
C. 1
D. 2
E. 4
Solution:
Multiplying the given equation by xyξ =0 yields x2y+2y=xy2+2x. Thus
x2yβ2xβxy2+2y=x(xyβ2)βy(xyβ2)=(xβy)(xyβ2)=0.
Because xβyξ =0, it follows that xy=2β.
The problems on this page are the property of the MAA's American Mathematics Competitions