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If $2 x^{1 / 3} + 2 x^{- 1 / 3} = 5$ , then $x =$

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3 or 1/9

8 or 1/8

5 or 1/5

2 or 1/5

answer is D.

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Detailed Solution

$2 x^{1 / 3} + 2 x^{- 1 / 3} = 5 \Rightarrow {(2 x^{1 / 3} + 2 x^{- 1 / 3})}^{3} = 5^{3} \Rightarrow 8 x + 8 x^{- 1} + 3 (2 x^{1 / 3}) (2 x^{- 1 / 3}) 5 = 125$

$\Rightarrow 8 x + 8 / x + 60 = 125 \Rightarrow 8 x^{2} - 65 x + 8 = 0 \Rightarrow (8 x - 1) (x - 8) = 0 \Rightarrow x = 8 o r 1 / 8$

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