Choose the correct answer from the alternatives given.
If $x^{2}$ + 3x + 1 = 0, then the value of $x^{3} + \frac{1}{x^{3}}$ is

-18

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-36

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Solution

The correct option is B -18
$x^{2}$ + 3x + 1 = 0
$x^{2}$ + 1 = -3x
Dividing it by x. we get
$x + \frac{1}{x} = - 3$
Cubing both the sides,
$x^{3} + \frac{1}{x^{3}} + 3 (x + \frac{1}{x}) - 27 \Rightarrow x^{3} + \frac{1}{x^{3}}$ = -27 3(-3) = -27 + 9 = -18

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