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 $x^2-7 x+1=0$ 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 $\left(x^2+\frac{1}{x^2}\right)=6$ 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 $x=\sqrt{–\sqrt{3}+\sqrt{3+8 \sqrt{7+4 \sqrt{3}}}}$ where $x > 0$, then the value of $x$ is equal to:

Option 1: 3

Option 2: 4

Option 3: 1

Option 4: 2

Question : If $x=\frac{1}{x-3},(x>0)$, then the value of $x+\frac{1}{x}$ is:

Option 1: $\sqrt{11}$

Option 2: $\sqrt{17}$

Option 3: $\sqrt{15}$

Option 4: $\sqrt{13}$