Question : If $x^{4}+\frac{1}{x^{4}}=119$, then the value of $x-\frac{1}{x}$ is:

Option 1: 6

Option 2: 12

Option 3: 11

Option 4: 3

Question : If $x-\frac{1}{x}=5, x \neq 0$, then what is the value of $\frac{x^6+3 x^3-1}{x^6-8 x^3-1} ?$

Option 1: $\frac{3}{8}$

Option 2: $\frac{13}{12}$

Option 3: $\frac{4}{9}$

Option 4: $\frac{11}{13}$

Question : If $x+\frac{1}{x}=5$, then the value of $\frac{x}{1+x+x^2}$ is:

Option 1: $\frac{1}{5}$

Option 2: $\frac{1}{6}$

Option 3: $5$

Option 4: $6$

Question : If $x=2+\sqrt3$, then the value of $\frac{x^{2}-x+1}{x^{2}+x+1}$ is:

Option 1: $\frac{2}{3}$

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

Option 3: $\frac{4}{5}$

Option 4: $\frac{3}{5}$

Question : If $x+\frac{1}{x}=6$, then find the value of $\frac{3 x}{2 x^2-5 x+2}$.

Option 1: $1$

Option 2: $\frac{3}{7}$

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

Option 4: $0$

Question : If $x-\frac{1}{x}=2$, then what is the value of $x^2+\frac{1}{x^2}$?

Option 1: 4

Option 2: 5

Option 3: 3

Option 4: 6