If x2 - 3x + 1 = 0, then the value of ( x^4 + 1x^2 ) ( x^2 + 5x + 1 ) is:

Answer: Option C

$$\begin{array}{rl}& x^2-3x+1=0\\ & x^2+1=3x\\ & x+\frac{1}{x}=3\\ & \Rightarrow \frac{\left(x^4+\frac{1}{x^2}\right)}{\left(x^2+5x+1\right)}\\ & =\frac{x\left(x^3+\frac{1}{x^3}\right)}{\left(x^2+1+5x\right)}\\ & =\frac{x\left[3^3-3\times 3\right]}{\left(3x+5x\right)}\\ & =\frac{x\left[18\right]}{\left(8x\right)}\\ & =\frac{9}{4}\end{array}$$