Question : If $x^{2} + \frac{1}{x^{2}} = 18$ and $x > 0$, what is the value of $x^{3} + \frac{1}{x^{3}}?$

Option 1: $36 \sqrt{5}$

Option 2: $40 \sqrt{5}$

Option 3: $46 \sqrt{5}$

Option 4: $34 \sqrt{5}$

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 $x=1+\sqrt{2}+\sqrt{3}$, then the value of $(2x^4-8x^3-5x^2+26x-28)$ is:

Option 1: $2\sqrt{2}$

Option 2: $3\sqrt{3}$

Option 3: $5\sqrt{5}$

Option 4: $6\sqrt{6}$

Question : If $x>0$ and $x^4+\frac{1}{x^4}=254$, what is the value of $x^5+\frac{1}{x^5}?$

Option 1: $717 \sqrt{2}$

Option 2: $723 \sqrt{2}$

Option 3: $720 \sqrt{2}$

Option 4: $726 \sqrt{2}$