Question

Solve the following inequality:
$x-\sqrt{1-|x|}<0.$

Answer 1

given $x-\sqrt{1-|x|}<0$ claearly it is satisfied for all negative values of x

and for $x>1$ is not valies $\because$ tne value in root becomes negative

for $x\in (0,1)$ eqyation becomes $x-\sqrt{1-x}<0$

$x<\sqrt{1-x}$

squaring on both sides we get $x^2+x-1<0$

$⟹x\in (-\infty ,\frac{\sqrt{5}-1}{2})$