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sudha Grade:
        

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)

6 years ago

Answers : (1)

Puneet Mittal AskiitiansExpert-IITD
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


Which is the answer.


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.



 

6 years ago
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