If $(x-2)$ is a factor of the polynomial $x^{3}-2ax^{2}+ax-1$,then find the value of $a$.

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

If $a+b+c=0,$ then the value of $\left(\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}\right)$ is:

If $x_{1} x_{2} x_{3} = 4(4 + x_{1} + x_{2} + x_{3})$,then what is the value of $\left[\frac{1}{(2 + x_{1})}\right] + \left[\frac{1}{(2 + x_{2})}\right] + \left[\frac{1}{(2 + x_{3})}\right]$?

If $a = \frac{1}{a-5}$ and $a > 0$,then the value of $a + \frac{1}{a}$ is

If $a-b=1$ and $ab=6$,then what is the value of $(a^3-b^3)$?