Question

Choose the correct answer from the alternatives given.
If $x=2^{\frac{1}{3}}+2^{\frac{-1}{3}}$ then the value of $2x^3-6x$ will be

• A. 5
• B. 6
• C. 8
• D. 10

Answer 1

The correct option is A 5

x = $2^{\frac{1}{3}}+2^{\frac{-1}{3}}$
$x=2^{\frac{1}{3}}+\frac{1}{2^{\frac{1}{3}}}$
Cubing both the sides,
$x^3=2+\frac{1}{2}+3(2^{\frac{1}{3}}+\frac{1}{2^{\frac{1}{3}}})$
$x^3=2+\frac{1}{2}+3\times x\Rightarrow x^3=\frac{4+1+6x}{2}$
$2x^3$ $-6x=5$.