Answer:
C
Step-by-step explanation:
Once
[tex]\sqrt{xy} = 6[/tex]
We know that [tex]xy = 36[/tex]
There are infinity values for [tex]x, y[/tex], but considering [tex]x, y \in \mathbb{Z}[/tex]
Below we have all the solutions for [tex]x, y[/tex]
Negative:
[tex]\\x = -36 \text{ and } y = -1\\x = -18 \text{ and } y = -2\\x = -12 \text{ and } y = -3\\x = -9 \text{ and } y = -4\\x = -6 \text{ and } y = -6\\x = -4 \text{ and } y = -9\\x = -3 \text{ and } y = -12\\x = -2 \text{ and } y = -18\\x = -1 \text{ and } y = -36\\[/tex]
Positives:
[tex]x = 36 \text{ and } y = 1\\x = 18 \text{ and } y = 2\\x = 12 \text{ and } y = 3\\x = 9 \text{ and } y = 4\\x = 6 \text{ and } y = 6\\x = 4 \text{ and } y = 9\\x = 3 \text{ and } y = 12\\x = 2 \text{ and } y = 18\\x = 1 \text{ and } y = 36\\[/tex]
We can see that [tex]x + y \neq 18[/tex]
