Everybody knows that polynomial equations of degrees three and four can be solved by radicals. But how to do it? Cardano’s formula for the roots of cubic equations is too complicated and hard to remember. Reduction of degree four equation to cubic equation also is not obvious. In the talk I will present simple solutions to the following problems.

$\textbf{Problem 1.}$ Assume that the cosine of an angle $\alpha$ is given. Find a cosine of $\frac{\alpha}{n}$ for a given natural $n$ using radical.

$\textbf{Problem 2.}$ Solve by radicals any system of two polynomial equations of degree two in two unknowns.

I will explain how solutions of these Problems imply solutions of cubic and quartic equations.