If ( a + 1/a ) = 6, then ( a^4 + 1a^4 ) = ?

Answer: Option A

$$\begin{array}{rl}& \left(a+\frac{1}{a}\right)=6\\ & \Rightarrow {\left(a+\frac{1}{a}\right)}^2=6^2\\ & =36\\ & \Rightarrow a^2+\frac{1}{a^2}+2=36\\ & \Rightarrow \left(a^2+\frac{1}{a^2}\right)=34\\ & \Rightarrow {\left(a^2+\frac{1}{a^2}\right)}^2={\left(34\right)}^2\\ & \Rightarrow a^4+\frac{1}{a^4}+2=1156\\ & \Rightarrow \left(a^4+\frac{1}{a^4}\right)=1154\end{array}$$