Question : If $x^2+\frac{1}{x^2}=7$, then the value of $x^3+\frac{1}{x^3}$ where x > 0 is equal to:

Option 1: 18

Option 2: 12

Option 3: 15

Option 4: 16

Question : If $x^2-\sqrt{7} x+1=0$, then what is the value of $x^5+\frac{1}{x^5} ?$

Option 1: $19 \sqrt{7}$

Option 2: $21 \sqrt{7}$

Option 3: $25 \sqrt{7}$

Option 4: $27 \sqrt{7}$

Question : If $2x=\sqrt{a}+\frac{1}{\sqrt{a}}, a>0$, then the value of $\frac{\sqrt{x^{2}-1}}{x-\sqrt{x^{2}-1}}$ is:

Option 1: $a+1$

Option 2: $\frac{1}{2}(a+1)$

Option 3: $\frac{1}{2}(a–1)$

Option 4: $a–1$

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: $\sqrt{13}$

Question : If $\frac{22 \sqrt{2}}{4 \sqrt{2}-\sqrt{3+\sqrt{5}}}=a+\sqrt{5} b$, with $a, b>0$, then what is the value of $(a b):(a+b)$?

Option 1: 7 : 8

Option 2: 7 : 4

Option 3: 4 : 7

Option 4: 8 : 7