Solve `x-sqrt(1-|x|) lt 0`.

Answer

`x in [-1,-(1)/(2)+(sqrt(5))/(2))`

Explanation

`x-sqrt(1-|x|) lt 0`
We must have `1-|x| ge 0`
`implies |x| le 1`
`implies x in [-1,1]`
Case I : `x in[0,1]`
So, we have `x lt sqrt(1-x)`
`implies x^(2)lt1-x`
`implies x^(2)+x-1 lt 0`
`implies (x+(1)/(2))^(2)-((sqrt(5))//(2))^(2) lt 0`
`implies x in[0,-(1)/(2)+(sqrt(5))/(2))` ..........`(i)`
Case II : `x in [-1,0)`
So, we have `x lt sqrt(1+x)`
`implies "negative " lt "positive"`
`implies x in [-1,0)`.........`(ii)`
Hence, from `(i)` and `(ii)`
`x in [-1,-(1)/(2)+(sqrt(5))/(2))`