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A binary operation * is defined on the set of real numbers, R by x *...

Further Mathematics
WAEC 2024

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

  • A. \(\frac{5}{12}\)
  • B. \(\frac{13}{12}\)
  • C. -\(\frac{5}{12}\)
  • D. -\(\frac{13}{12}\)
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Correct Answer: Option A
Explanation

Given:  x * y = \(\frac{y^2 - x^2}{2xy}\), Evaluate -3 * 2

-3 * 2 → x = -3, y = 2

-3 * 2 =   \(\frac{y^2 - x^2}{2xy}\) =  \(\frac{(2^2 - (-3)^2}{2 \times 2 \times -3}\)

= \(\frac{4 - 9}{- 12}\) = \(\frac{-5}{-12}\) = \(\frac{5}{12}\)


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