Question : If $\left(x^2+\frac{1}{x^2}\right)=7$, and $0<x<1$, find the value of $x^2-\frac{1}{x^2}$.

Option 1: $3 \sqrt{5}$

Option 2: $4 \sqrt{5}$

Option 3: $-4\sqrt{3}$

Option 4: $-3\sqrt{5}$

Question : If $\left(x^2+\frac{1}{x^2}\right)=6$ and $0<x<1$, what is the value of $x^4-\frac{1}{x^4}$?

Option 1: $24\sqrt{2}$

Option 2: $-24\sqrt{2}$

Option 3: $-12\sqrt{10}$

Option 4: $12\sqrt{10}$

Question : If $x^2-7 x+1=0$ and $0<x<1$, what is the value of $x^2-\frac{1}{x^2}?$

Option 1: $21\sqrt{5}$

Option 2: $-21\sqrt{5}$

Option 3: $28\sqrt{5}$

Option 4: $-28\sqrt{5}$

Question : If $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$, what is the value of $x$?

Option 1: $\frac{5}{2}$

Option 2: $\frac{25}{3}$

Option 3: $4$

Option 4: $3$

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: $108\sqrt{3}$