If $(\sqrt{3}+i)^{10}=a+b i, a, b \in \mathbf{R}$, then the values of $a$ and $b$ are respectively

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 $a x^2+b x+c=0$ then $\left(\frac{\alpha}{a \beta+b}\right)^3-\left(\frac{\beta}{a \alpha+b}\right)^3=$

The maximum value of $\left\{x \in \mathbf{R} / \sqrt{x+2}>\sqrt{8-x^2}\right\}=$