Question

$\sqrt{x} + \sqrt{x - \sqrt{1 - x \: } } = 1 \: find \: the \: value \: of \: x$

Answer 1

okay so your answer is here...

$\sqrt{x} + \sqrt{x - \sqrt{1 - x} } = 1 \\ \\ \sqrt{x} - 1 = - \sqrt{x - \sqrt{1 - x} } \\ sq \: both \: sides \\ x + 1 - 2 \sqrt{x} = x - \sqrt{1 - x} \\ 1 - 2 \sqrt{x} = - \sqrt{1 - x} \\ sq.again \\ 1 + 4x - 4 \sqrt{x} = 1 - x \\ 5x - 4 \sqrt{x} = 0 \\ \sqrt{x} (5 \sqrt{x} - 4) = 0 \\ \\ either \: x = 0 \: or \: 5 \sqrt{x} = 4 \: \: x = \frac{16}{25}$
hope it will help you.