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JAMB 1998 · UME · Q12

Solve the equation x−x−2−1=0\sqrt x - \sqrt{x - 2} - 1 = 0.

Worked solution (try it first)
  1. Isolate one root: x=1+x−2\sqrt x = 1 + \sqrt{x - 2}.
  2. Square both sides: x=1+2x−2+x−2x = 1 + 2\sqrt{x - 2} + x - 2.
  3. The xx terms cancel: 2x−2=12\sqrt{x - 2} = 1, so x−2=12\sqrt{x - 2} = \frac12.
  4. Square again: x−2=14x - 2 = \frac14, so x=94x = \frac94, option D.

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