Problem:
For real numbers a and b, define a$b=(a−b)2. What is (x−y)2$(y−x)2 ?
Answer Choices:
A. 0
B. x2+y2
C. 2x2
D. 2y2
E. 4xy
Solution:
Note that (y−x)2=(x−y)2, so
(x−y)2$(y−x)2=(x−y)2$(x−y)2=((x−y)2−(x−y)2)2=02=0
The problems on this page are the property of the MAA's American Mathematics Competitions