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

Option 1: $11$

Option 2: $18$

Option 3: $47$

Option 4: $51$

Question : If $x^4+x^{-4}=47, x>0$, then what is the value of $x+\frac{1}{x}-2?$

Option 1: 1

Option 2: 0

Option 3: 5

Option 4: 3

Question : What is the value of $\frac{x^2-x-6}{x^2+x-12}÷\frac{x^2+5x+6}{x^2+7x+12}$?

Option 1: $1$

Option 2: $\frac{(x-3)}{(x+3)}$

Option 3: $\frac{(x+4)}{(x-3)}$

Option 4: $\frac{(x-3)}{(x+4)}$

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 $x^2+\frac{1}{x^2}=\frac{7}{4}$ 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: $\sqrt{3}$