Question : If $(x+\frac{1}{x})^2=3$, then what is the value of $x^6 + x^{–6}$?

Option 1: 6

Option 2: 2

Option 3: –6

Option 4: –2

Question : If $(x+\frac{1}{x})=–2$, then the value of $(x^7+\frac{1}{x^7})$ is:

Option 1: 1

Option 2: –1

Option 3: 0

Option 4: –2

Question : If $(x-\frac{1}{x})^2=\sqrt3$, then the value of $(x^6+\frac{1}{x^6})$ equals:

Option 1: 90

Option 2: 100

Option 3: 110

Option 4: 120

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

Option 1: $\frac{2}{7}$

Option 2: $\frac{7}{8}$

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

Option 4: $\frac{8}{7}$

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: $0$