If x^2 + 1x^2 = 1 , then the value of x^102 + x^96 + x^90 + x^84 + x^78 + x^72 + 5 is?

Answer: Option B

$$\begin{array}{rl}& x^2+\frac{1}{x^2}=1\\ & \text{Then, }{\left(x+\frac{1}{x}\right)}^2=1+2\\ & \Rightarrow x+\frac{1}{x}=\sqrt{3}\\ & \Rightarrow x^3+\frac{1}{x^3}\\ & ={\left(\sqrt{3}\right)}^3-3\sqrt{3}\\ & =3\sqrt{3}-3\sqrt{3}\\ & =0\\ & \text{Then,}\\ & x^{102}+x^{96}+x^{90}+x^{84}+x^{78}+x^{72}+5\end{array}$$
  $$=x^{96}\left(x^6+1\right)+$$    $$x^{84}\left(x^6+1\right)+$$   $$x^{72}\left(x^6+1\right)+$$   $$5$$
  $$=5$$