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The roots of the equation $x^{2 / 3} + x^{1 / 3} - 2 = 0$ are

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$1, - 8$

1, 4

$1, - 4$

1, 8

answer is C.

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Detailed Solution

$x^{2 / 3} + x^{1 / 3} - 2 = 0 \Rightarrow {(x^{1 / 3})}^{2} + 1 (x^{1 / 3}) - 2 = 0$

Let $a = x^{1 / 3},$ then $a^{2} + a - 2 = 0 \Rightarrow a = 1, - 2$

Hence $x = 1, - 8$ (by $a = x^{1 / 3}$ ).

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