If x2 - 4x + 1 = 0, then what is the value of x9 + x7 - 194x5 - 194x3?

Answer: Option B

$$\begin{array}{rl}& x^2-4x+1=0\\ & x+\frac{1}{x}=4\\ & x^2+\frac{1}{x^2}=14\\ & x^4+\frac{1}{x^4}=194\\ & x^9+x^7-194x^5-194x^3\\ & x^9+x^7-\left(x^4+\frac{1}{x^4}\right)x^5-\left(x^4+\frac{1}{x^4}\right)x^3\\ & =x^9+x^7-x^9-x-x^7-\frac{1}{x}\\ & =-\left(x+\frac{1}{x}\right)\\ & =-4\end{array}$$