Solve `x >sqrt((1-x))`

Explanation

Given ineqquality can be solved by squaring both sides But sometimes squaring gives which do not satisy the original inequality.Before squaring we must restrict x for which terms in the given inequailty are well defined .
` x gt sqrt(1-x).` Here x must be positive .
Now `sqrt(1- x)` is defined only when `1- x ge 0 or x le 1`
squaring given inequality both sides `x^2 gt -x `
`rArr x^2 + x-1 gt 0 `
`rarr (x -(-1-sqrt(5))/2)(x-(-1+sqrt(5))/2)gt 0 `

`rArr x lt (-1 -sqrt(5))/(2) of x gt (-1+ sqrt(5))/2`
From (1) and (2) , ` x in ( sqrt(5-1)/2, (1)]`