Problem:
If y+4=(x−2)2, x+4=(y−2)2, and xî€ =y, what is the value of x2+y2?
Answer Choices:
A. 10
B. 15
C. 20
D. 25
E. 30
Solution:
Expanding the binomials and subtracting the equations yields x2−y2=3(x−y). Because x−yî€ =0, it follows that x+y=3. Adding the equations gives x2+y2=5(x+y)=5â‹…3=(B)15​.
Note: The two solutions are (x,y)=(23​+221​​,23​−221​​) and (23​−221​​,23​+221​​).