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

Option 1: 198

Option 2: 216

Option 3: 180

Option 4: 234

Question : If $\left(x+\frac{1}{x}\right)=2 \sqrt{2}$ and $x>1$, what is the value of $\left(x^6-\frac{1}{x^6}\right)$?

Option 1: $140\sqrt{2}$

Option 2: $116\sqrt{2}$

Option 3: $144\sqrt{2}$

Option 4: $128\sqrt{2}$

Question : If $\left(x-\frac{1}{x}\right)^2=12$, what is the value of $\left(x^2-\frac{1}{x^2}\right)$, given that $x>0$?

Option 1: $6 \sqrt{2}$

Option 2: $8 \sqrt{3}$

Option 3: $6 \sqrt{3}$

Option 4: $8 \sqrt{2}$

Question : If $\left(x^2 - \frac{1}{x^2}\right) = 4 \sqrt{6}$ and $x>1$, what is the value of $\left(x^3 - \frac{1}{x^3}\right)?$

Option 1: $20 \sqrt{2}$

Option 2: $24 \sqrt{2}$

Option 3: $18 \sqrt{2}$

Option 4: $22 \sqrt{2}$

Question : If $\left(x+\frac{1}{x}\right)=\sqrt{6}$ and $x>1$, what is the value of $\left(x^8-\frac{1}{x^8}\right)$?

Option 1: $120\sqrt{3}$

Option 2: $128\sqrt{3}$

Option 3: $112\sqrt{3}$

Option 4: $108\sqrt{3}$

Question : If $\left(x - \frac{1}{x}\right) = 2 \sqrt{2}$, what is the value of $\left(\mathrm{x}^6 + \frac{1}{\mathrm{x}^6}\right)$?

Option 1: 1030

Option 2: 960

Option 3: 1000

Option 4: 970