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

Answer: Option B

$$\begin{array}{rl}& x^2-5x+1=0\\ & \left(x^4+\frac{1}{x^2}\right)÷\left(x^2+1\right)=?\\ & x^2-5x+1=0\\ & \Rightarrow x+\frac{1}{x}=5\\ & \Rightarrow x^3+\frac{1}{x^3}=110\\ & \frac{x\left(x^3+\frac{1}{x^3}\right)}{x\left(x+\frac{1}{x}\right)}=\frac{110}{5}=22\end{array}$$