If x + 1/x = 5, then what is the value of x^6 + 1x^6?

Answer: Option C

$$\begin{array}{rl}& x+\frac{1}{x}=5\\ & \text{Cubing both sides, we get}\\ & x^3+\frac{1}{x^3}+3\times x\times \frac{1}{x}\left(x+\frac{1}{x}\right)=125\\ & x^3+\frac{1}{x^3}+3\times 5=125\\ & x^3+\frac{1}{x^3}=110\\ & \text{Squaring both sides, we get}\\ & x^6+\frac{1}{x^6}+2=12100\\ & x^6+\frac{1}{x^6}=12098\end{array}$$