If x + 1/x = 3 + 12, then what is the value of x^4 + 1x^4?

Answer: Option C

$$\begin{array}{rl}& x+\frac{1}{x}=\frac{\sqrt{3}+1}{2}\\ & x^2+\frac{1}{x^2}={\left(\frac{\sqrt{3}+1}{2}\right)}^2-2\\ & =\frac{4+2\sqrt{3}}{4}-2\\ & =\frac{4+2\sqrt{3}-8}{4}\\ & =\frac{-4+2\sqrt{3}}{4}\\ & =\frac{-2+\sqrt{3}}{2}\\ & x^4+\frac{1}{x^4}={\left(\frac{-2+\sqrt{3}}{2}\right)}^2-2\\ & =\frac{4+3-4\sqrt{3}-8}{4}\\ & =\frac{-1-4\sqrt{3}}{4}\end{array}$$