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OAU Post-UTME Mathematics 2011 Question 14

Question 14

Surds

Given that a = 1/(2 − √3), b = 1/(2 + √3), find the value of a2 + b2

  1. A.14/37
  2. B.7
  3. C.142√3
  4. D.14
Show the answer and explanation

Answer: D (14)

Explanation

Rationalising, a = 2 + √3 and b = 2 − √3. a² + b² = (7 + 4√3) + (7 − 4√3) = 14.