Система уравнений: (x+y)(x+y+z)=72 (y+z)(x+y+z)=120 (x+z)(x+y+z)=96

   1. Обозначим:

      p = x + y + z;

• {(x + y)(x + y + z) = 72;{(y + z)(x + y + z) = 120;{(x + z)(x + y + z) = 96;
• {p(p - z) = 72;{p(p - x) = 120;{p(p - y) = 96.

   2. Сложим все уравнения:

• p(3p - x - y - z) = 72 + 120 + 96;
• p(3p - p) = 288;
• 2p^2 = 288;
• p^2 = 144;
• p = ±12.

   3. Выразим x, y и z через p:

• {p - z = 72/p;{p - x = 120/p;{p - y = 96/p;
• {z = p - 72/p;{x = p - 120/p;{y = p - 96/p.

   a) p = -12;

• {z = -12 + 72/12;{x = -12 + 120/12;{y = -12 + 96/12;
• {z = -6;{x = -2;{y = -4;

   b) p = 12;

• {z = 12 - 72/12;{x = 12 - 120/12;{y = 12 - 96/12;
• {z = 6;{x = 2;{y = 4.

   Ответ: (-2; -4; -6); (2; 4; 6).