Question : If $x=\sqrt{\frac{2+\sqrt3}{2-\sqrt3}}$, then what is the value of $(x^{2}+x-9)$?

Option 1: 0

Option 2: $3\sqrt2$

Option 3: $3\sqrt3$

Option 4: $5\sqrt3$

Question : If $x=\sqrt2+1$, then the value of $x^{4}-\frac{1}{x^{4}}$ is:

Option 1: $8\sqrt2$

Option 2: $18\sqrt2$

Option 3: $6\sqrt2$

Option 4: $24\sqrt2$

Question : If $x=2+\sqrt3$, then the value of $\frac{x^{2}-x+1}{x^{2}+x+1}$ is:

Option 1: $\frac{2}{3}$

Option 2: $\frac{3}{4}$

Option 3: $\frac{4}{5}$

Option 4: $\frac{3}{5}$

Question : When $2x+\frac{2}{x}=3$, then the value of ($x^3+\frac{1}{x^3}+2)$ is:

Option 1: $\frac{2}{7}$

Option 2: $\frac{7}{8}$

Option 3: $\frac{7}{2}$

Option 4: $\frac{8}{7}$

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

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3