Question : If $x^2+\frac{1}{x^2}=29$, then find the value of $x-\frac{1}{x}$.

Option 1: $\pm 4$

Option 2: $\pm 3 \sqrt{3}$

Option 3: $\pm 3$

Option 4: $\pm 4 \sqrt{3}$

Question : If $x=\sqrt{3}-\frac{1}{\sqrt{3}}, y=\sqrt{3}+\frac{1}{\sqrt{3}}$, then the value of $\frac{x^2}{y}+\frac{y^2}{x}$ is:

Option 1: $\sqrt{3}$

Option 2: $3\sqrt{3}$

Option 3: $16\sqrt{3}$

Option 4: $2\sqrt{3}$

Question : If $x^{4}+\frac{1}{x^{4}}=16$, then what is the value of $x^{2}+\frac{1}{x^{2}}$?

Option 1: $3 \sqrt{2}$

Option 2: $2 \sqrt{2}$

Option 3: $5 \sqrt{2 }$

Option 4: $4 \sqrt{2}$

Question : If $x=(\sqrt{6}-1)^{\frac{1}{3}}$, then the value of $\left(x-\frac{1}{x}\right)^3+3\left(x-\frac{1}{x}\right)$ is:

Option 1: $\frac{2 \sqrt{6}-6}{5}$

Option 2: $\frac{4 \sqrt{6}-6}{5}$

Option 3: $\frac{4 \sqrt{6}-6}{3}$

Option 4: $\frac{4 \sqrt{3}-6}{5}$

Question : If $x=\frac{4\sqrt{15}}{\sqrt{5}+\sqrt{3}}$, the value of $\frac{x+\sqrt{20}}{x–\sqrt{20}}+\frac{x+\sqrt{12}}{x–\sqrt{12}}$ is:

Option 1: $1$

Option 2: $2$

Option 3: $\sqrt{3}$

Option 4: $\sqrt{5}$