d=[tex] \left[\begin{array}{ccc}x2&x1&x3\\x3&x2&x1\\x1&x3&x2\end{array}\right] = \\ \\
Aduni. coloanele .2 .si. 3. la. 1:
(x1+x2+x3) \left[\begin{array}{ccc}1&x1&x3\\1&x2&x1\\1&x3&x2\end{array}\right] = \\ \\
dezvolti. determinantul
(x1+x2+x3)[( x1^2+x2^2+x3^2)-(x1x2+x1x3+x2x3)][/tex]
Srii rel lui VIETE:
(1) x1+x2+x3=2
x1x2+x1x3+x2x3=0
x1x2x3=2
ridici prima relatie la patrat
x1^2+x2^2+x3^2+2(x1x2+x2x3+x1x3)=4
x1^2+x2^2+x3^2=4-2*0=4
Inlocuiesti in d= 4(4-0)=16
