Explicație pas cu pas:
[tex]x(x + 1) + y(y - 1) + z(z - 3) \leqslant - \frac{11}{4} \\ [/tex]
[tex]4x(x + 1) + 4y(y - 1) + 4z(z - 3) + 11 \leqslant 0 \\ [/tex]
[tex]{4x}^{2} + 4x + 1 + {4y}^{2} - 4y + 1 + {4z}^{2} - 12z + 9\leqslant 0 \\ [/tex]
[tex]{(2x + 1)}^{2} + {(2y - 1)}^{2} + {(2z - 3)}^{2} \leqslant 0 \\ [/tex]
→
[tex]2x + 1 = 0 = > x = - \frac{1}{2} \\ [/tex]
[tex]2y - 1 = 0 = > y = \frac{1}{2} \\ [/tex]
[tex]2z - 3 = 0 = > z = \frac{3}{2} \\ [/tex]
⇒
[tex]m_{a} = \frac{x + y + z}{3} \\ = \frac{ - 0.5 + 0.5 + 1.5}{3} = \frac{1.5}{3} = 0.5 \\ [/tex]
