$hpt \Leftrightarrow \begin{cases}x=1-y \\ (1-y)^4+y^4+(1-y)^3-y^3-(1-y)^2-y^2=0 \end{cases}$$ \Leftrightarrow \begin{cases}x=1-y \\ (y^2-y+1)(2y^2-2y+1)=0 \end{cases}$
$\Leftrightarrow\begin{cases}x=1-y \\ y=1\pm \frac 1{\sqrt2}\end{cases}$
$\Leftrightarrow(x;y)=\{(\frac{\sqrt 2}2;\frac{2-\sqrt 2}2);(\frac{-\sqrt2}2;\frac {2+\sqrt2}2\}$