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

Option 1: 1

Option 2: 0

Option 3: 3

Option 4: 2

Question : If $x^{2} -3x +1=0$, then the value of $\frac{\left(x^4+\frac{1}{x^2}\right)}{\left(x^2+5 x+1\right)}$ is:

Option 1: $\frac{9}{4}$

Option 2: $\frac{27}{8}$

Option 3: $\frac{5}{2}$

Option 4: $2$

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

Option 1: –1

Option 2: –2

Option 3: 1

Option 4: 2

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

Option 1: 9

Option 2: –9

Option 3: 1

Option 4: 2

Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{3z}+\frac{y^3}{3xz}+\frac{z^2}{3x}$?

Option 1: $0$

Option 2: $xz$

Option 3: $y$

Option 4: $3y$

Question : If $(x+\frac{1}{x})\neq 0$ and $(x^3+\frac{1}{x^3})= 0$, then the value $(x+\frac{1}{x})^4$ is:

Option 1: 9

Option 2: 12

Option 3: 15

Option 4: 16