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 $x^4+x^{-4}=47, x>0$, then what is the value of $x+\frac{1}{x}-2?$

Option 1: 1

Option 2: 0

Option 3: 5

Option 4: 3

Question : If $x^2-\sqrt{7} x+1=0$, then $\left(x^3+x^{-3}\right)=?$

Option 1: $4 \sqrt{7}$

Option 2: $3 \sqrt{7}$

Option 3: $10 \sqrt{7}$

Option 4: $7 \sqrt{7}$

Question : If $x^2-3 x+1=0$, then the value of $\left(x^4+\frac{1}{x^2}\right) \div\left(x^2+1\right)$ is:

Option 1: 5

Option 2: 6

Option 3: 9

Option 4: 7