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For all real values of x if |(x^2- 3x-1...

For all real values of x if `|(x^2- 3x-1)/(x^2+x+1)| < 3` limit of x are

Text Solution

Verified by Experts

Given
`|(x^2- 3x-1)/(x^2+x+1)| < 3`
=`-3< (x^2- 3x-1)/(x^2+x+1)<3`
so,`(x^2- 3x-1)<3(x^2+x+1)`
=`(x^2- 3x-1)< 3x^2+3x+3`
=`2x^2+6x+4>0`
=`(x+2)(x+1)>0...(1)`
also,`(x^2- 3x-1)/(x^2+x+1)>-3`
...
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