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WAEC Further Mathematics 2025 Question 13

Question 13

Binary Operations

The operation * is defined on the set of real numbers, R, by x * y = (√x − √y)/(2√x + 3√y), where x, y > 0. Evaluate 7 * 4

  1. A.13/4 + (5/4)√7
  2. B.−13/4 + (5/4)√7
  3. C.13/4 − (5/4)√7
  4. D.−13/4 − (5/4)√7
Show the answer and explanation

Answer: B (−13/4 + (5/4)√7)

Explanation

7 * 4 = (√7 − 2)/(2√7 + 6). Multiply top and bottom by (2√7 − 6): (14 − 10√7 + 12)/(28 − 36) = (26 − 10√7)/(−8) = −13/4 + (5/4)√7.