Question

If $x = 2^{1/3} - 2^{- 1/3},$ then $2x^{3} + 6x =$

• A. 1
• B. 2
• C. 3
• D. None of these

Answer 1

Answer: (C)

3

Answer 2

$x = 2^{1/3} - 2^{- 1/3}$

$\Rightarrow$ $x^{3} = 2 - 2^{- 1} - 3.2^{1/3}.2^{- 1/3}(2^{1/3} - 2^{- 1/3})$

$\Rightarrow$ $x^{3} = 2 - \frac{1}{2} - 3x$ ⇒ $x^{3} + 3x = \frac{3}{2}$

$\therefore$ $2x^{3} + 6x = 3$.