Question : If $\left(x-\frac{1}{x}\right) =4$, then what is the value of $\left(x^6+\frac{1}{x^6}\right)$?

Option 1: 4689

Option 2: 4786

Option 3: 5832

Option 4: 5778

Question : What is the value of $\frac{1+\mathrm{x}}{1-\mathrm{x}^2} \div \frac{1+\mathrm{x}}{1-\mathrm{x}^4}-\frac{1-\mathrm{x}^4}{1-\mathrm{x}} \times \frac{1+\mathrm{x}}{1-\mathrm{x}^2}$?

Option 1: $\frac{2 \mathrm{x}\left(1+\mathrm{x}^2\right)}{(1-\mathrm{x})}$

Option 2: $\frac{2 \mathrm{x}\left(1+\mathrm{x}^2\right)}{(\mathrm{x}-1)}$

Option 3: $(1-\mathrm{x})^2$

Option 4: $\left(1+\mathrm{x}^2\right)$

Question : If $\left(x-\frac{1}{x-2}\right)=7$, then the value of $(x-2)^3-\frac{1}{(x-2)^3}$ is:

Option 1: 130

Option 2: 115

Option 3: 140

Option 4: 125

Question : If $x^2-\sqrt{9.76} x+1=0$ and $x>1$, then the value of $\left(x^3-\frac{1}{x^3}\right)$ is:

Option 1: 21.042

Option 2: 24.024

Option 3: 21.024

Option 4: 24.042

Question : If $\small p^{3}-q^{3}=\left (p-q \right )\left \{ \left (p-q \right)^{2}-xpq \right \}$, then find the value of $x$.

Option 1: 3

Option 2:  –3

Option 3: 1

Option 4:  –1