WAEC Further Mathematics 2025 Objective — Question 13

Question 13 of 40 from the West African Examinations Council (WAEC) Further Mathematics 2025 Objective paper, with the correct answer and a full explanation.

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.

A. 13/4 + 5/4√7
B. -13/4 + 5/4√7Correct
C. 13/4 - 5/4√7
D. -13/4 - 5/4√7

Explanation

7*4 = (√7-2)/(2√7+6). Rationalising by multiplying by the conjugate (2√7-6) gives (-13+5√7)/4, i.e. -13/4 + 5/4√7.

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