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Question

Find the interval of x such that x23x1x2+x+1<3 is satisfied is


  1. (,2)(1,)

  2. [85,2][52,]

  3. (5,2)(2,5)

  4. None of these


Solution

The correct option is A

(,2)(1,)


As x2+x+1>0x, we get |x23x1|<3(x2+x+1)

3(x2+x+1)<x23x1<3(x2+x+1)
2<4x2 and 2x2+6x+4>0
x2+3x+2>0
x < -2 or x > -1

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