Final answer:
After simplifying the expression using the given ratio x/y = -2, we find that the square root of (x^2 / y^2 + y^2 / x^2) is the square root of 17 divided by 2. However, none of the provided answer choices match this result, indicating an error in the choices.
Step-by-step explanation:
If x/y = -2, we are asked to find the square root of (x^2 / y^2 + y^2 / x^2). To solve this, we first simplify the expression inside the square root:
x^2 / y^2 = (-2)^2 = 4 (since x/y = -2)
Now, because x/y = -2, y/x = -1/2, so y^2 / x^2 = (-1/2)^2 = 1/4.
Adding these together, we get:
4 + 1/4 = 16/4 + 1/4 = 17/4
To find the square root, we calculate:
\( \sqrt{17/4} = \sqrt{17}/\sqrt{4} = \sqrt{17}/2 \)
However, none of the answer choices (a) 2, (b) 4, (c) 6, or (d) 8 match \( \sqrt{17}/2 \), which indicates there may have been a typo or omission in the choices provided. The correct answer is not listed.