Solve for the equation \(\sqrt{x}\) - \(\sqrt{(x - 2)}\) - 1 = 0
A
\(\frac{3}{2}\)
B
\(\frac{2}{3}\)
C
\(\frac{4}{9}\)
D
\(\frac{9}{4}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\sqrt{x}\) - \(\sqrt{(x - 2)}\) - 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 = \(\frac{9}{4}\)
Source: Myschool Past Questions Archive (Record #30674)