Question

If $a-\frac{1}{3}=\frac{1}{a}$ then the value of $a^3-\frac{1}{a^3}$ is

• A. $1\frac{1}{27}$
• B. $1\frac{2}{27}$
• C. $1\frac{3}{27}$
• D. $1\frac{4}{27}$

Answer 1

The correct option is A $1\frac{1}{27}$

Given $a-\frac{1}{3}=\frac{1}{a}$

=$a-\frac{1}{a}=\frac{1}{3}$

We know that

$x^3-y^3=(x-y{)}^3+3xy(x+y)$

Then $a^3-{\left(\frac{1}{a}\right)}^3=(a-\left(\frac{1}{a}\right){)}^3+3a\left(\frac{1}{a}\right)(a+\left(\frac{1}{a}\right))$

=${\left(\frac{1}{3}\right)}^3+3\times \left(\frac{1}{3}\right)$

=$\frac{1}{27}+1=\frac{28}{27}=1\frac{1}{27}$