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

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

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

Question : If $\frac{1}{6}$ of $x$ – $\frac{7}{2}$ of $\frac{3}{7}$ equals to $(-\frac{7}{4})$, then the value of $x$ is:

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