If a3 + 3a2 + 9a = 1, then what is the value of a^3 + 3/a?

Answer: Option C

$$\begin{array}{rl}& a^3+3a^2+9a=\mathrm{1.......}\left(\text{i}\right)\\ & a^3+\frac{3}{a}=?\\ & \text{Multiply by ’}a\text{’ and ’3’ in equation}\left(\text{i}\right)\\ & \left(a^3+3a^2+9a=1\right)\times a\\ & \left(a^3+3a^2+9a=1\right)\times 3\\ & a^4+3a^3+9a^2=1\times a\\ & \underline{3a^3+9a^2+27a=1\times 3}\to \left(\text{Subtracting}\right)\\ & a^4-27a=a-3\\ & a^4+3=28a\\ & \text{On dividing by }a\\ & a^3+\frac{3}{a}=28\end{array}$$