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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