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: $1024 \sqrt{15}$

Option 2: $992 \sqrt{15}$

Option 3: $998 \sqrt{15}$

Option 4: $1012 \sqrt{15}$

Question : If $\left(x+\frac{1}{x}\right)=5$, and $x>1$, what is the value of $\left(x^8-\frac{1}{x^8}\right)?$

Option 1: $60605 \sqrt{21}$

Option 2: $60615 \sqrt{21}$

Option 3: $60705 \sqrt{21}$

Option 4: $60725 \sqrt{21}$