Question : If $x+\frac{1}{x}=-6$, what will be the value of $x^5+\frac{1}{x^5}$?

Option 1: – 7776

Option 2: – 6726

Option 3: – 6738

Option 4: – 6732

Question : If $(-\frac{1}{2}) \times (x-5) + 3 = -\frac{5}{2}$, then what is the value of $x$?

Option 1: 16

Option 2: 4

Option 3: – 6

Option 4: – 4

Question : If $(x+\frac{1}{x})^2=3$, then what is the value of $x^6 + x^{–6}$?

Option 1: 6

Option 2: 2

Option 3: –6

Option 4: –2

Question : If $x+\frac{1}{x}=5$, then the value of $\frac{x}{1+x+x^2}$ is:

Option 1: $\frac{1}{5}$

Option 2: $\frac{1}{6}$

Option 3: $5$

Option 4: $6$

Question : If $x+5+\frac{1}{x+1}=6$, then the value of $(x+1)^{3}+\frac{1}{(x+1)^{3}}$ is:

Option 1: 2

Option 2: 0

Option 3: –2

Option 4: 4