Question

$a=\sqrt[3]{3\sqrt{2}+1}-\sqrt[3]{3\sqrt{2}-1}$ then the value of $a^3+3a-2$ is__

• A. $3$
• B. $0$
• C. $2$
• D. $1$

Answer 1

The correct option is B $0$

$a=\sqrt[3]{3\sqrt{2}+1}-\sqrt[3]{3\sqrt{2}-1}$

cubing both sides, we get

$a^3={(\sqrt[3]{3\sqrt{2}+1}-\sqrt[3]{3\sqrt{2}-1})}^3$

$a^3=\sqrt{2}+1-\sqrt{2}+1-3\times \sqrt[3]{3\sqrt{2}+1}\times \sqrt[3]{3\sqrt{2}-1}\left((\sqrt[3]{3\sqrt{2}+1}-\sqrt[3]{3\sqrt{2}-1})\right)$

$a^3=2-3\times \sqrt[3]{32-1}a$

$a^3=2-3a$

$a^3+3a-2=0$