The Context Panel option Solve≻Solve (explicit) gives the four solutions $k\=\pm 1\,\left(x\,y\right)\=\left(0\,0\right)$ and $k\=5\/4\,\left(x\,y\right)\=\left(\pm \sqrt{3}\/2\,3\/4\right)$, but the option Solve≻Solve returns the second two solutions in the form

 $\left\{k\=\frac{5}{4}\,x\=\frac{1}{2}\mathrm{RootOf}\left({\mathrm{\_Z}}^2-3\right)\,y\=\frac{3}{4}\right\}$

The RootOf structure is a compressed representation of an algebraic number, that is, a number that is the solution of a polynomial equation. The Context Panel option All Values applies the allvalues command, which converts the RootOf to the algebraic number(s) it represents.

It might seem that Maple has returned six solutions, not four. However, the solutions for $k\=\pm 1$ are repeated, so there are actually only four distinct solutions.