Question

If $2a-\frac{3}{a}=1$, then, find the value of $8a^3-\frac{27}{a^3}$

• A. $19$
• B. $20$
• C. $21$
• D. $22$

Answer 1

The correct option is A

$19$

Given: $2a-\frac{3}{a}=1$

$\Rightarrow {(2a-\frac{3}{a})}^3=1$

$\Rightarrow (2a{)}^3-\frac{3^3}{a^3}-3\times 2a\times \frac{3}{a}\times (2a-\frac{3}{a})=1$

$\Rightarrow 8a^3-\frac{27}{a^3}-18\times 1=1$

$\Rightarrow 8a^3-\frac{27}{a^3}=1+18=19$