If x2 - √7x + 1 = 0, then what is the value of x^5 + 1x^5?

Answer: Option A

$$\begin{array}{rl}& x^2-\sqrt{7}x+1=0\\ & x^2+1=\sqrt{7}x\\ & x+\frac{1}{x}=\sqrt{7}\\ & x^5+\frac{1}{x^5}=\left(x^2+\frac{1}{x^2}\right)\left(x^3+\frac{1}{x^3}\right)-\left(x+\frac{1}{x}\right)\\ & =\left({\left(\sqrt{7}\right)}^2-2\right)\left({\left(\sqrt{7}\right)}^3-3\times \sqrt{7}\right)-\sqrt{7}\\ & =5\times 4\sqrt{7}-\sqrt{7}\\ & =19\sqrt{7}\end{array}$$