Question

If $(a+\frac{1}{a})=12$, then $(a^3+\frac{1}{a^3})$ is equal to:-

• A. $1680$
• B. $1686$
• C. $1698$
• D. $1692$

Answer 1

The correct option is D $1692$

We have,

$(a+\frac{1}{a})=12$

On taking cube both sides, we get

${(a+\frac{1}{a})}^3={12}^3$

$a^3+\frac{1}{a^3}+3(a+\frac{1}{a})=1728$

$a^3+\frac{1}{a^3}+3\times 12=1728$

$a^3+\frac{1}{a^3}+36=1728$

$a^3+\frac{1}{a^3}=1692$

Hence, this is the answer.