If $\alpha, \beta$ and $\gamma$ are the roots of $x^3 + 8 = 0$,then the equation whose roots are $\alpha^2, \beta^2$ and $\gamma^2$ is

The sum of the $162^{\text{th}}$ power of the roots of the equation $x^{3}-2x^{2}+2x-1=0$ is

If $\alpha$ is a non-real root of the equation $x^6-1=0$,then $\frac{\alpha^2+\alpha^3+\alpha^4+\alpha^5}{\alpha+1} = $

If $z$ is a complex number such that $z^2+z+1=0$,then $\left(z+\frac{1}{z}\right)^3+\left(z^2+\frac{1}{z^2}\right)^3+\left(z^3+\frac{1}{z^3}\right)^3+\ldots+\left(z^{2020}+\frac{1}{z^{2020}}\right)^3=$

If $\alpha, \beta$ are the roots of the quadratic equation $x^2+x+1=0$,then the equation whose roots are $\alpha^{19}, \beta^7$ is

If $\sqrt{x}+\frac{1}{\sqrt{x}}=2 \cos \theta$,then $x^6+x^{-6}=$