If 1/a ( a^2 + 1 ) = 3 , then the value of a^6 + 1a^3 = ?

Answer: Option B

$$\begin{array}{rl}& \frac{1}{a}\left(a^2+1\right)=3\\ & \Rightarrow a+\frac{1}{a}=3\\ & \Rightarrow a^3+\frac{1}{a^3}+3.a.\frac{1}{a}\left(a+\frac{1}{a}\right)=3^3\\ & \Rightarrow a^3+\frac{1}{a^3}+3\left(3\right)=3^3\\ & \Rightarrow a^3+\frac{1}{a^3}=27-9\\ & \Rightarrow a^3+\frac{1}{a^3}=18\\ & \Rightarrow \frac{a^6+1}{a^3}=18\end{array}$$