~ 交流數學姿色 : 立體名稱 , 方程組 ~

1 正四面體﹐立方體(正六面體)﹐正八面體﹐正十二面體﹐正二十面體Tetrahedron﹐Cube(hexahedron)﹐Octahedron﹐Dodecahedron﹐Icosahedron

2 重新整理方程組

(x + z - y)(y + z - x) = 3

(x + y - z)(x + z - y) = 6

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

(x + y - z)(x + z - y) = (y + z - x)(x + y - z)(x + z - y)(y + z - x)

(y + z - x)^2 = 1

因此y + z - x = -1 或 1

若y + z - x = -1

x = y + z + 1

因此(x - y)^2 = z^2 - 3

(z + 1)^2 = z^2 - 3

2z + 1 = -3

z = -2

然後(z - x)^2 = y^2 - 2

(y + 1)^2 = y^2 - 2

2y + 1 = - 2

y = -3/2

因此x = -5/2

若y + z - x = 1

x = y + z - 1

因此(x - y)^2 = z^2 - 3

(z - 1)^2 = z^2 - 3

-2z + 1 = -3

z = 2

然後(z - x)^2 = y^2 - 2

(1 - y)^2 = y^2 - 2

-2y + 1 = - 2

y = 3/2

因此x = 5/2

綜合(x,y,z) = (5/2,3/2,2) 或(-5/2,-3/2,-2)