Problem:
Given that x and y are distinct nonzero real numbers such that x+x2​=y+y2​, what is xy ?
Answer Choices:
A. 41​
B. 21​
C. 1
D. 2
E. 4
Solution:
Multiplying the given equation by xyî€ =0 yields x2y+2y=xy2+2x. Thus
x2y−2x−xy2+2y=x(xy−2)−y(xy−2)=(x−y)(xy−2)=0.
Because x−yî€ =0, it follows that xy=2​.
The problems on this page are the property of the MAA's American Mathematics Competitions