Question : If $x^4+\frac{1}{x^4}=1154$, where $x>0$, then what is the value of $x^3+\frac{1}{x^3}?$

Option 1: 205

Option 2: 214

Option 3: 185

Option 4: 198

Question : if $x+\frac{1}{x}=2$, then the value of $x^4+\frac{1}{x^4}$=__________.

Option 1: 0

Option 2: 2

Option 3: –1

Option 4: 1

Question : If $\frac{1}{x+2}=\frac{3}{y+3}=\frac{1331}{z+1331}=\frac{1}{3}$, then what is the value of $\frac{x}{x+1}+\frac{y}{y+6}+\frac{z}{z+2662}$?

Option 1: $0$

Option 2: $1$

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

Option 4: $3$

Question : If $x + \frac{1}{x} = \sqrt{3}$, then the value of $x^{18} + x^{12} + x^{6} + 1$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

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

Option 1: 4

Option 2: 5

Option 3: 6

Option 4: 8