If $a = x^{1 / 3} - x^{- 1 / 3},$ then $(a^{3} + 3 a)$ is equal to

x - x^{- 1}

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x^{- 1} - x

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x + x^{- 1}

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x^{- 1} + x

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Solution

The correct option is A $x - x^{- 1}$
$a = x^{1 / 3} - \frac{1}{x^{1 / 3}}$
$a^{3} = x - \frac{1}{x} - 3 (x^{1 / 3} - x^{- 1 / 3})$
$a^{3} = x - x^{- 1} - 3 a$
$a^{3} + 3 a = x - x^{- 1}$

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Similar questions

a = x^{1 / 3} - x^{- 1 / 3}

a^{3} + 3 a =

If p = x $^{1 / 3}$ + x $^{- 1 / 3}$ , then p $^{3}$ - 3p is equal to

{(\frac{x + 1}{x^{2 / 3} + x^{1 / 3} + 1} - \frac{x - 1}{x - x^{1 / 2}})}^{10}

x

x

{(\frac{x + 1}{x^{2 / 3} - x^{1 / 3} + 1} - \frac{x - 1}{x - x^{1 / 2}})}^{10}

x \neq 0, 1

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