A binary operation * is defined on the set of real numbers, R by x * y = \(\frac{y^2 – x^2}{2xy}\), x, y ≠ 0, where x and y are real numbers. Evaluate -3 * 2
-
\(\frac{5}{12}\)
- \(\frac{13}{12}\)
- -\(\frac{5}{12}\)
- -\(\frac{13}{12}\)
The correct answer is: A
Explanation
Given: x * y = \(\frac{y^2 - x^2}{2xy}\), Evaluate -3 * 2
-3 * 2 → x = -3, y = 2
-3 * 2 = \(\frac{y^2 - x^2}{2xy}\) = \(\frac{(2^2 - (-3)^2}{2 \times 2 \times -3}\)
= \(\frac{4 - 9}{- 12}\) = \(\frac{-5}{-12}\) = \(\frac{5}{12}\)