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Solve `x-sqrt(1-|x|) lt 0`. |
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Answer» Correct Answer - `x in [-1,-(1)/(2)+(sqrt(5))/(2))` `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))` |
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