Решите систему уравнения

(x+y) * (x+y+z) = 72

(y+z) * (x+y+z) = 120

(z+x) * (x+y+z) = 96

Нужно сложить каждую строчку

(x+y) (x+y+z) + (y+z) (x+y+z) + (x+z) (x+y+z) 72 + 120 + 96

(x+y+z) ((x+y) + (y+z) + (x+z)) = 288

(x+y+z) (2x+2y+2z) = 288

(x+y+z) 2 (x+y+z) = 288

(x+y+z) ^2 = 144

x+y+z = + - 12

x1 = 12-y-z x2 = - 12-y-z

Далее подставляем

2-y-z+y) (12-y-z+y+z) = 72 (-12-y-z+y) (-12-y-z+y+z) = 72

(y+z) 12 = 120 (y+z) (-12) = 120

(12-y-z+z) 12 = 96 (-12-y-z+z) (-12) = 96

(12-z) 12 = 72 (-12-z) (-12) = 72

(y+z) 12 = 120 (y+z) (-12) = 120

(12-y) 12 = 96 (12-y) (-12) = 96

12-z = 6 - 12-z = - 6

y+z = 10 y+z = - 10

12-y = 8 - 12-y = - 8

z = 12-6=6 z = - 12+6 = - 6

y = 12-8=4 y = - 12+8 = - 4

x1 = 12-6-4 = 2 x2 = - 12 - (-6) - (-4) = - 2

z = 12-6=6 z 1 = - 12+6 = - 6

y = 12-8=4 y1 = - 12+8 = - 4

x1 = 12-6-4 = 2 x2 = - 12 - (-6) - (-4) = - 2