Home » Solve for the equation (sqrt{x}) – (sqrt{(x – 2)}) – 1 = 0

Solve for the equation (sqrt{x}) – (sqrt{(x – 2)}) – 1 = 0

Solve for the equation (sqrt{x}) – (sqrt{(x – 2)}) – 1 = 0
  • A.
    (frac{3}{2})
  • B.
    (frac{2}{3})
  • C.
    (frac{4}{9})
  • D.
    (frac{9}{4})
Correct Answer: Option D
Explanation

(sqrt{x}) – (sqrt{(x – 2)}) – 1 = 0
= (sqrt{x}) – (sqrt{(x – 2)}) = 1
= ((sqrt{x}) – (sqrt{(x – 2)}))2 = 1
= x – 2 (sqrt{x(x – 2)}) + x -2 = 1
= (2x – 3)2 = [2 (sqrt{x(x – 4)})]2
= 4x2 – 12x + 9
= 4(x2 – 2x)
= 4x2 – 12x + 9
= 4x2 – 8x
4x = 9
x = (frac{9}{4})

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