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}
= 4x^{2} – 12x + 9
= 4(x^{2} – 2x)
= 4x^{2} – 12x + 9
= 4x^{2} – 8x
4x = 9
x = (frac{9}{4})