Simplest Cubic Fields

Let $Q(alpha)$ be the simplest cubic field, it is known that $Q(alpha)$ can be generated by adjoining a root of the irreducible equation $x^{3}-kx^{2}+(k-3)x+1=0$, where $k$ belongs to $Q$. In this paper we have established a relationship between $alpha$, $alpha$ and $k,k$ where $alpha$ is a root of the equation $x^{3}-kx^{2}+(k-3)x+1=0$ and $alpha$ is a root of the same equation with $k$ replaced by $k$ and $Q(alpha)=Q(alpha)$.