JAMB - Mathematics (1998 - No. 10)
Solve for the equation \(\sqrt{x}\) - \(\sqrt{(x - 2)}\) - 1 = 0
\(\frac{3}{2}\)
\(\frac{2}{3}\)
\(\frac{4}{9}\)
\(\frac{9}{4}\)
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 = \(\frac{9}{4}\)
= \(\sqrt{x}\) - \(\sqrt{(x - 2)}\) = 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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