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JAMB Mathematics 1988 Question 10

Question 10

Surds

Find m such that (m + √3)(1 − √3)2 = 6 − 2√3.

  1. A.1
  2. B.2
  3. C.3
  4. D.4
Show the answer and explanation

Answer: C (3)

Explanation

(1 − √3)² = 4 − 2√3. Expanding (m + √3)(4 − 2√3) = 4m − 6 + (4 − 2m)√3. Matching with 6 − 2√3 gives 4m − 6 = 6, so m = 3 (and 4 − 2m = −2 checks).