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 $x^2-\sqrt{7} x+1=0$, 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 $x^2+\frac{1}{x^2}=\frac{7}{4}$ 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 $x^2-9x+1=0$, what is the value of $(x^3+\frac{1}{x^3})$?

Option 1: $54$

Option 2: $108$

Option 3: $702$

Option 4: $810$