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WAEC Further Mathematics 2013 Question 7

Question 7

Surds

If √x + √(x + 1) = √(2x + 1), find the possible value of x.

  1. A.1 and −1
  2. B.1 and 2
  3. C.1 and 2
  4. D.0 and −1
Show the answer and explanation

Answer: D (0 and −1)

Explanation

Squaring: 2x + 1 + 2√(x(x + 1)) = 2x + 1, so x(x + 1) = 0 and x = 0 or −1. Only D contains these values (and x = 0 is the one that checks in the real numbers).