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`        The set of values for which x^3+1 greater than or equal to x^2 +x is (ans x greater than or equal to -1)`
7 years ago

22 Points
```										Dear Sudha,
The solution to your euqation is as follows:
x3 + 1 ≥ x2 + x
x3 - x2 - x + 1 ≥ 0
x3 + 1 - x(x +1 ) ≥ 0
(x+1)( x2 -x +1 ) - x(x+1) ≥ 0
Takign x+1 in common,
(x+1)(x2 -x +1 -x) ≥ 0
(x+1)(x2 -2x +1) ≥ 0
(x+1)(x-1)2  ≥ 0
Since (x-1)2 is greater than eual to zero for all values of x ( as (x-1)2 is always postive ),therefore
(x+1)(x-1)2  ≥ 0 will happen when (x+1) ≥ 0
i.e x+1 ≥ 0
x ≥ -1
Solved by : Puneet
Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

```
7 years ago
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