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

Option 1: $0$

Option 2: $2$

Option 3: $-2$

Option 4: $-1$

Question : If $a= \frac{\sqrt{x+2}+\sqrt{x-2}}{\sqrt{x+2}-\sqrt{x-2}}$, then the value of $(a^{2}-ax)$ is:

Option 1: 1

Option 2: 2

Option 3: –1

Option 4: 0

Question : If $p = 5 + 2\sqrt6$,  then  $\frac{\sqrt p - 1}{\sqrt p}$ is:

Option 1: $1 + \sqrt2 - \sqrt3$

Option 2: $1 - \sqrt2 + \sqrt3$

Option 3: $ - 1 + \sqrt2 - \sqrt3$

Option 4: $1 - \sqrt2 - \sqrt3$