Question : If $x^2-7x+1=0$, what is the value of $(x+\frac{1}{x})$.

Option 1: 7

Option 2: 3

Option 3: 51

Option 4: 47

Question : If for a non-zero $x$, $3x^{2}+5x+3=0,$ then the value of $x^{3}+\frac{1}{x^{3}}$ is:

Option 1: $\frac{10}{27}$

Option 2: $-\frac{10}{27}$

Option 3: $\frac{2}{3}$

Option 4: $-\frac{2}{3}$

Question : If $\frac{1}{x+2}=\frac{3}{y+3}=\frac{1331}{z+1331}=\frac{1}{3}$, then what is the value of $\frac{x}{x+1}+\frac{y}{y+6}+\frac{z}{z+2662}$?

Option 1: $0$

Option 2: $1$

Option 3: $\frac{3}{2}$

Option 4: $3$

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:

Option 1: 4

Option 2: 5

Option 3: 6

Option 4: 8

Question : If $x^2-2\sqrt{10}x+1=0$, what is the value of $(x-\frac{1}{x})$?

Option 1: $4$

Option 2: $6$

Option 3: $3$

Option 4: $5$