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WAEC Further Mathematics 2021 Question 1

Question 1

Surds

Simplify: (1/(2 − √3) + 2/(2 + √3))−1

  1. A.−1/33 (6 + √3)
  2. B.−1/33 (6 − √3)
  3. C.1/33 (6 + √3)
  4. D.1/33 (6 − √3)
Show the answer and explanation

Answer: C (1/33 (6 + √3))

Explanation

1/(2 − √3) = 2 + √3 and 2/(2 + √3) = 2(2 − √3) = 4 − 2√3, so the sum is 6 − √3. Its reciprocal is (6 + √3)/(36 − 3) = (6 + √3)/33.