If x^24 + 1x^12 = 7, then the value of x^72 + 1x^36 = \,?

Answer: Option D

$$\begin{array}{rl}& \frac{x^{24}+1}{x^{12}}=7\left(\text{Given}\right)\\ & \Rightarrow \frac{x^{24}}{x^{12}}+\frac{1}{x^{12}}=7\\ & \Rightarrow x^{12}+\frac{1}{x^{12}}=7\\ & \text{Cubing both sides}\\ & \Rightarrow {\left(x^{12}+\frac{1}{x^{12}}\right)}^3=7^3\end{array}$$
  $$\Rightarrow x^{36}+\frac{1}{x^{36}}+\frac{3\times x^{12}\times 1}{x^{12}}$$     $$\left(x^{12}+\frac{1}{x^{12}}\right)=$$    $$343$$
$$\begin{array}{rl}& \Rightarrow x^{36}+\frac{1}{x^{36}}+3\left(7\right)=343\\ & \Rightarrow x^{36}+\frac{1}{x^{36}}=343-21\\ & \Rightarrow x^{36}+\frac{1}{x^{36}}=322\\ & \Rightarrow \frac{x^{72}+1}{x^{36}}=322\end{array}$$