Question : If $x^2-5 x+1=0$, then the value of $\left(x^4+\frac{1}{x^2}\right) \div\left(x^2+1\right)$ is:

Question : If $\frac{x^{2}-x+1}{x^{2}+x+1}=\frac{2}{3}$, then the value of $\left (x+\frac{1}{x} \right)$ is:

Question : If $x^2-3 x+1=0$, then the value of $\left(x^4+\frac{1}{x^2}\right) \div\left(x^2+1\right)$ is:

Question : The next term of the sequence $\left (1+\frac{1}{2} \right):\left (1+\frac{1}{2} \right) \left (1+\frac{1}{3} \right): \left (1+\frac{1}{2} \right)\left (1+\frac{1}{3} \right)\left (1+\frac{1}{4} \right): .........$ is:

Question : The value of $\left(5 \div 2\right.$ of $\left.\frac{1}{2}\right)+\left(5 \frac{1}{4} \div \frac{3}{7}\right.$ of $\left.\frac{1}{2}\right) \div\left(5 \frac{1}{9}-7 \frac{7}{8} \div 9 \frac{9}{20}\right) \times \frac{11}{21}$ is: