if x and y are numbers such that ( x + 6 ) ( y - 6 ) = 0, what is the smallest possible value of x ^ 2 + y ^ 2
Choose the correct choice from the following answers
A) 0	B) 16	C) 25	D) 36	E) 49
<gadget id="calculator">6 ** 2</gadget>
<output>36</output>

<result>D</result>
if x and y are numbers such that ( x + 6 ) ( y - 6 ) = 0, what is the smallest possible value of x ^ 2 + y ^ 2
power(6, 2)
from ( x + 6 ) ( y - 6 ) = 0 it follows that either x = - 6 or y = 6 . thus either x ^ 2 = 36 or y ^ 2 = 36 . now , if x ^ 2 = 36 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 36 + 0 = 36 . similarly if y ^ 2 = 36 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 36 = 36 . answer : d .