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)

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

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