Question : If $(a+\frac{1}{a})^{2}=3$, then the value of $(a^{6}-\frac{1}{a^{6}})$ will be:

Option 1: 1

Option 2: 3

Option 3: 0

Option 4: 2

Question : If $x+\frac{1}{x}=\sqrt{3}$, the value of $(x^{18}+x^{12}+x^{6}+1)$ is:

Option 1: 0

Option 2: 1

Option 3: 2

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 $\frac{1}{a}(a^2+1)=3$, then the value of $\frac{a^6+1}{a^3}$ is:

Option 1: 9

Option 2: 18

Option 3: 27

Option 4: 1

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: $0$