Problem:
Real numbers x and y satisfy the equation x2+y2=10x−6y−34. What is x+y?
Answer Choices:
A. 1
B. 2
C. 3
D. 6
E. 8
Solution:
By completing the square the equation can be rewritten as follows:
x2+y2=10x−6y−34,x2−10x+25+y2+6y+9=0,(x−5)2+(y+3)2=0.​
Therefore x=5 and y=−3, so x+y=(B)2​.
The problems on this page are the property of the MAA's American Mathematics Competitions