Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$; then what is the value of $x+\frac{1}{x}$?

Option 1: $2$

Option 2: $\frac{\sqrt{15}}{2}$

Option 3: $\sqrt{5}$

Option 4: $\sqrt{3}$

Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$, what is the value of $(x^3+\frac{1}{x^3})$?

Option 1: $\frac{3\sqrt{3}}{5}$

Option 2: $\frac{3\sqrt{15}}{5}$

Option 3: $\frac{3\sqrt{15}}{8}$

Option 4: $\frac{3\sqrt{5}}{8}$

Question : If $x^4+\frac{1}{x^4}=1154$, where $x>0$, then what is the value of $x^3+\frac{1}{x^3}?$

Option 1: 205

Option 2: 214

Option 3: 185

Option 4: 198

Question : If $\sqrt{x}+\frac{1}{\sqrt{x}}=3, x>0$, then $x^2\left(x^2-47\right)=?$

Option 1: $0$

Option 2: $2$

Option 3: $-2$

Option 4: $-1$

Question : If $x^4+x^{-4}=194, x>0$, then the value of $x+\frac{1}{x}$ is:

Option 1: 14

Option 2: 6

Option 3: 4

Option 4: 8