One of the roots of the equation $x^{14}+x^9-x^5-1=0$ is

If $\left(\frac{1+i}{1-i}\right)^{\frac{m}{2}}=\left(\frac{1+i}{i-1}\right)^{\frac{n}{3}}=1$ where $m, n \in N$,then the greatest common divisor of the least values of $m$ and $n$ is:

For the equation $x^2 + x + 1 = 0$,if $\alpha$ and $\beta$ are the roots,then which of the following equations has roots $\alpha^{19}$ and $\beta^{7}$?

The product of all the roots of ${\left( \cos \frac{\pi }{3} + i\sin \frac{\pi }{3} \right)^{3/4}}$ is

For any real number $n \in \mathbb{R}$,$(\cosh x + \sinh x)^n =$

Let $A_r = \left(x+\frac{1}{x}\right)^3 \cdot \left(x^2+\frac{1}{x^2}\right)^3 \cdot \left(x^3+\frac{1}{x^3}\right)^3 \cdots \left(x^r+\frac{1}{x^r}\right)^3$. If $x^2+x+1=0$,then $\frac{1}{A_3}+\frac{1}{A_6}+\frac{1}{A_9}+\frac{1}{A_{12}}+\cdots \infty =$