Răspuns:
Explicație pas cu pas:
[tex]\texttt{Fie r ratia progresiei aritmetice.}\\\begin{vmatrix}1&1&1\\x&y&z\\z&y&x\end{vmatrix}\stackrel{\bold{\stackrel{C_1:C_1-C_2}{C_2:C_2-C_3}}}{=}\begin{vmatrix}0&0&1\\-r&-r&z\\r&r&x\end{vmatrix}\stackrel{\texttt{dezvoltare dupa prima linie}}{===========}\begin{vmatrix}-r&-r\\r&r\end{vmatrix}=\\=-r\cdot r+r\cdot r=-r^2+r^2=\boxed{0}[/tex]
