Question

If $a=2^{\frac{1}{3}}-2^{\frac{-1}{3}}$, then find the value of $2a^3+6a-3$.

• A. $1$
• B. $0$
• C. $3$
• D. $2$

Answer 1

Answer: (B)

$0$

$a^3={(\sqrt[3]{32}-(\frac{1}{\sqrt[3]{32}}\left)\right)}^3=\left(\sqrt[3]{32}\right)-\left(\frac{1}{\sqrt[3]{32}}\right)-3.\sqrt[3]{32}.\left(\frac{1}{\sqrt[3]{32}}\right)[\sqrt[3]{32}-(\frac{1}{\sqrt[3]{32}}\left)\right]a^3=2-\left(\frac{1}{2}\right)-3\left(a\right)2a^3=4-1-6aor2a^3+6a-3=0$