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If x2 - 1 <...

Question

If $x^{2} - 1 < x^{3}$ then, for which of the following values is the above inequality true?

x = - 3

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x = - 2

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x = - 1

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x = 0

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Solution

The correct option is D $x = 0$
Given inequality is $x^{2} - 1 < x^{3}$
By further solving given equation we get
$\Rightarrow$ $x^{3} - x^{2} + 1 > 0$
This equation hold for all positive values of $x$ include zero
But does not hold for negative values
Hence, option D is correct.

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