Question : If $\frac{x^2+1}{x}=5$, then find the value of $x^4+\frac{1}{x^4}-36$.

Option 1: 491

Option 2: 149

Option 3: 419

Option 4: 194

Question : If $x+\frac{1}{x}=2$, then find the value of $x^{1823}+\frac{1}{x^{1929}}$.

Option 1: 2

Option 2: 1

Option 3: 0

Option 4: –1

Question : If $x=\frac{1}{x-5}(x>0)$, then the value of $x+\frac{1}{x}$ is:

Option 1: $\sqrt{41}$

Option 2: $\sqrt{29}$

Option 3: $\sqrt{23}$

Option 4: $\sqrt{43}$

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 $x>1$ and $x+\frac{1}{x}=2\frac{1}{12}$, then the value of $x^{4}-\frac{1}{x^{4}}$ is:

Option 1: $\frac{58975}{20736}$

Option 2: $\frac{59825}{20736}$

Option 3: $\frac{57985}{20736}$

Option 4: $\frac{57895}{20736}$