The solution of x+x−1−x=1 is

x+x−1−x=1x−1−x=1−xx−1−x=1+x−2x1−x=1−2x1−x=1+4.x−4.x5x=4x16x=25x2x(25x−16)=025x2−16x=0x=0(neglected) and x=1625

The solution of x+x−1−x=1 is

x+x−1−x=1x−1−x=1−xx−1−x=1+x−2x1−x=1−2x1−x=1+4.x−4.x5x=4x16x=25x2x(25x−16)=025x2−16x=0x=0(neglected) and x=1625

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The solution of $\sqrt{x} + \sqrt{x - \sqrt{1 - x}} = 1$ is

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$\frac{25}{16}$

$\frac{16}{25}$

answer is D.

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Detailed Solution

$\sqrt{x} + \sqrt{x - \sqrt{1 - x}} = 1$

$\sqrt{x - \sqrt{1 - x}} = 1 - \sqrt{x}$

$x - \sqrt{1 - x} = 1 + x - 2 \sqrt{x}$

$\sqrt{1 - x} = 1 - 2 \sqrt{x}$

$1 - x = 1 + 4. x - 4. \sqrt{x}$

$5 x = 4 \sqrt{x}$

$16 x = 25 x^{2}$

$x (25 x - 16) = 0$

$25 x^{2} - 16 x = 0$

$x = 0 (neglected) and x = \frac{16}{25}$

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The solution of $\sqrt{x} + \sqrt{x - \sqrt{1 - x}} = 1$ is