If x and y are numbers such that (x+3)(y-3)=0, what is the smallest possible value of x^2 + y^2  Answers:
A) 0
B) 3
C) 6
D) 9
E) 12

Rationale: "from ( x + 3 ) ( y - 3 ) = 0 it follows that either x = - 3 or y = 3 . thus either x ^ 2 = 9 or y ^ 2 = 9 . now , if x ^ 2 = 9 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 9 + 0 = 9 . similarly if y ^ 2 = 9 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 9 = 9 . answer : d ."
Answer: D