(x + y + z)² = (x + y)² + 2(x + y)z + z² = x² + 2xy + y² + 2xz + 2yz + z² = x² + y² + z² + 2(xy + xz + yz)
x² + xy + xz = y x(x + y + z) = y
y² + yz + yx = z y(x + y + z) = z
z² + zx + zy = x z(x + y + z) = x
всё складываем
x² + xy + xz + y² + yz + yx + z² + zx + zy = z + y + x
x² + y² +z² + 2(xy + xz + yz) = x + y + z
(x + y + z)² = x + y + z
1. x + y + z = 0
x(x + y + z) = y
y(x + y + z) = z
z(x + y + z) = x
0x = y
0y = z
0z = x
x=y=z=0
2. x + y + z = 1
x = y
y = z
z = x
x² + x² + x² = x
3x² = x
x = 0 y = 0 y = 0
x = 3 не корень
ответ (0 0 0)
y ' = 0
3x^2 - 8x = 0
x (3x - 8) = 0
x = 0 ;
3x - 8 = 0
3x = 8
x = 8/3
ответ
2