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 is D

\(\sqrt{x}\) - \(\sqrt{(x - 2)}\) - 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 = \(\frac{9}{4}\)