If ( a^4 + 1a^4 ) = 1154, then the value of ( a^3 + 1a^3 ) is = ?

Answer: Option A

$$\begin{array}{rl}& \left(a^4+\frac{1}{a^4}\right)\text{ = 1154}\\ & \left(\text{Adding}\text{2}\text{in}\text{both}\text{sides}\right)\\ & \Rightarrow a^4+\frac{1}{a^4}+2=1156\\ & \Rightarrow {\left(a^2+\frac{1}{a^2}\right)}^2=1156\\ & \Rightarrow \left(a^2+\frac{1}{a^2}\right)=34\\ & \left(\text{Adding}\text{2}\text{in}\text{both}\text{sides}\right)\\ & \Rightarrow a^2+\frac{1}{a^2}+2=36\\ & \Rightarrow {\left(a+\frac{1}{a}\right)}^2=36\\ & \Rightarrow a+\frac{1}{a}=6\\ & \Rightarrow {\left(a+\frac{1}{a}\right)}^3=6^3=216\\ & \Rightarrow a^3+\frac{1}{a^3}+3.a.\frac{1}{a}\left(a+\frac{1}{a}\right)=216\\ & \Rightarrow a^3+\frac{1}{a^3}+3\times 6=216\\ & \Rightarrow a^3+\frac{1}{a^3}=216-18\\ & \Rightarrow a^3+\frac{1}{a^3}=198\end{array}$$