Question

y=
$y \sqrt{x { + \sqrt{x - 1} }^{2} }$
​

Answer 1

$= = > \: \: y = y \sqrt{x + {( \sqrt{x + 1}) }^{2} } \\ \\ = = > \: \: \frac{y}{y} = \sqrt{x + {x}^{2} + {1}^{2} + 2x } \\ \\ = = > \: \: \sqrt{ {x}^{2} + 3x + 1} = 1 \\ \\ \mathtt{Squaring \: both \: sides} \\ \\ = = > \: \: {x}^{2} + 3x + 1 = 1 \\ \\ = = > \: \: {x}^{2} + 3x = 0 \\ \\ = = > \: \: x(x + 3) = 0 \\ \\ \mathtt{ On \: comparing} \\ \\ x = 0 \: \: \: \: \: \mathtt{ \: or \: } \: \: \: \: x + 3 = 0 \\ \\ x = 0 \: \: \: or \: \: \: x \: = - 3$