好吧问答库 > 已知X+Y+Z=7，XY+YZ+ZX=14，XYZ=8 (X+Y)(Y+Z)(Z+X)的值

已知X+Y+Z=7，XY+YZ+ZX=14，XYZ=8 (X+Y)(Y+Z)(Z+X)的值

已知X+Y+Z=7，XY+YZ+ZX=14，XYZ=8(X+Y)(Y+Z)(Z+X)的值...

2026年09月21日 07:17

有2个网友回答

网友（1）：

[x,y,z]=solve('x+y+z=7','x*y+y*z+z*x=14','x*y*z=8*(x+y)*(y+z)*(x+z)')

x =

-1/3*(1078+7*23709^(1/2))^(1/3)-7/3/(1078+7*23709^(1/2))^(1/3)+14/3-1/18/(1078+7*23709^(1/2))^(2/3)*(-21*(1078+7*23709^(1/2))^(1/3)-3234-21*23709^(1/2)+42*(1078+7*23709^(1/2))^(2/3)+3*i*(147*(1078+7*23709^(1/2))^(2/3)-15092*(1078+7*23709^(1/2))^(1/3)-98*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+6971475+45276*23709^(1/2)-28*(1078+7*23709^(1/2))^(4/3))^(1/2))
-1/3*(1078+7*23709^(1/2))^(1/3)-7/3/(1078+7*23709^(1/2))^(1/3)+14/3-1/18/(1078+7*23709^(1/2))^(2/3)*(-21*(1078+7*23709^(1/2))^(1/3)-3234-21*23709^(1/2)+42*(1078+7*23709^(1/2))^(2/3)-3*i*(147*(1078+7*23709^(1/2))^(2/3)-15092*(1078+7*23709^(1/2))^(1/3)-98*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+6971475+45276*23709^(1/2)-28*(1078+7*23709^(1/2))^(4/3))^(1/2))
1/6*(1078+7*23709^(1/2))^(1/3)+7/6/(1078+7*23709^(1/2))^(1/3)+14/3-1/2*i*3^(1/2)*(1/3*(1078+7*23709^(1/2))^(1/3)-7/3/(1078+7*23709^(1/2))^(1/3))-1/36/(1078+7*23709^(1/2))^(2/3)*(-3234*i*3^(1/2)+21*i*(1078+7*23709^(1/2))^(1/3)*3^(1/2)-21*i*3^(1/2)*23709^(1/2)+21*(1078+7*23709^(1/2))^(1/3)+84*(1078+7*23709^(1/2))^(2/3)+3234+21*23709^(1/2)+3*(90552*i*3^(1/2)*23709^(1/2)+13942950*i*3^(1/2)+13942950+294*(1078+7*23709^(1/2))^(2/3)-294*i*3^(1/2)*(1078+7*23709^(1/2))^(2/3)+90552*23709^(1/2)+60368*(1078+7*23709^(1/2))^(1/3)+392*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+112*(1078+7*23709^(1/2))^(4/3))^(1/2))
1/6*(1078+7*23709^(1/2))^(1/3)+7/6/(1078+7*23709^(1/2))^(1/3)+14/3-1/2*i*3^(1/2)*(1/3*(1078+7*23709^(1/2))^(1/3)-7/3/(1078+7*23709^(1/2))^(1/3))-1/36/(1078+7*23709^(1/2))^(2/3)*(-3234*i*3^(1/2)+21*i*(1078+7*23709^(1/2))^(1/3)*3^(1/2)-21*i*3^(1/2)*23709^(1/2)+21*(1078+7*23709^(1/2))^(1/3)+84*(1078+7*23709^(1/2))^(2/3)+3234+21*23709^(1/2)-3*(90552*i*3^(1/2)*23709^(1/2)+13942950*i*3^(1/2)+13942950+294*(1078+7*23709^(1/2))^(2/3)-294*i*3^(1/2)*(1078+7*23709^(1/2))^(2/3)+90552*23709^(1/2)+60368*(1078+7*23709^(1/2))^(1/3)+392*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+112*(1078+7*23709^(1/2))^(4/3))^(1/2))
1/6*(1078+7*23709^(1/2))^(1/3)+7/6/(1078+7*23709^(1/2))^(1/3)+14/3+1/2*i*3^(1/2)*(1/3*(1078+7*23709^(1/2))^(1/3)-7/3/(1078+7*23709^(1/2))^(1/3))-1/36/(1078+7*23709^(1/2))^(2/3)*(3234*i*3^(1/2)-21*i*(1078+7*23709^(1/2))^(1/3)*3^(1/2)+21*i*3^(1/2)*23709^(1/2)+21*(1078+7*23709^(1/2))^(1/3)+84*(1078+7*23709^(1/2))^(2/3)+3234+21*23709^(1/2)+3*(-90552*i*3^(1/2)*23709^(1/2)-13942950*i*3^(1/2)+13942950+294*(1078+7*23709^(1/2))^(2/3)+294*i*3^(1/2)*(1078+7*23709^(1/2))^(2/3)+90552*23709^(1/2)+60368*(1078+7*23709^(1/2))^(1/3)+392*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+112*(1078+7*23709^(1/2))^(4/3))^(1/2))
1/6*(1078+7*23709^(1/2))^(1/3)+7/6/(1078+7*23709^(1/2))^(1/3)+14/3+1/2*i*3^(1/2)*(1/3*(1078+7*23709^(1/2))^(1/3)-7/3/(1078+7*23709^(1/2))^(1/3))-1/36/(1078+7*23709^(1/2))^(2/3)*(3234*i*3^(1/2)-21*i*(1078+7*23709^(1/2))^(1/3)*3^(1/2)+21*i*3^(1/2)*23709^(1/2)+21*(1078+7*23709^(1/2))^(1/3)+84*(1078+7*23709^(1/2))^(2/3)+3234+21*23709^(1/2)-3*(-90552*i*3^(1/2)*23709^(1/2)-13942950*i*3^(1/2)+13942950+294*(1078+7*23709^(1/2))^(2/3)+294*i*3^(1/2)*(1078+7*23709^(1/2))^(2/3)+90552*23709^(1/2)+60368*(1078+7*23709^(1/2))^(1/3)+392*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+112*(1078+7*23709^(1/2))^(4/3))^(1/2))

y =

1/3*(1078+7*23709^(1/2))^(1/3)+7/3/(1078+7*23709^(1/2))^(1/3)+7/3
1/3*(1078+7*23709^(1/2))^(1/3)+7/3/(1078+7*23709^(1/2))^(1/3)+7/3
-1/6*(1078+7*23709^(1/2))^(1/3)-7/6/(1078+7*23709^(1/2))^(1/3)+7/3+1/2*i*3^(1/2)*(1/3*(1078+7*23709^(1/2))^(1/3)-7/3/(1078+7*23709^(1/2))^(1/3))
-1/6*(1078+7*23709^(1/2))^(1/3)-7/6/(1078+7*23709^(1/2))^(1/3)+7/3+1/2*i*3^(1/2)*(1/3*(1078+7*23709^(1/2))^(1/3)-7/3/(1078+7*23709^(1/2))^(1/3))
-1/6*(1078+7*23709^(1/2))^(1/3)-7/6/(1078+7*23709^(1/2))^(1/3)+7/3-1/2*i*3^(1/2)*(1/3*(1078+7*23709^(1/2))^(1/3)-7/3/(1078+7*23709^(1/2))^(1/3))
-1/6*(1078+7*23709^(1/2))^(1/3)-7/6/(1078+7*23709^(1/2))^(1/3)+7/3-1/2*i*3^(1/2)*(1/3*(1078+7*23709^(1/2))^(1/3)-7/3/(1078+7*23709^(1/2))^(1/3))

z =

1/18/(1078+7*23709^(1/2))^(2/3)*(-21*(1078+7*23709^(1/2))^(1/3)-3234-21*23709^(1/2)+42*(1078+7*23709^(1/2))^(2/3)+3*i*(147*(1078+7*23709^(1/2))^(2/3)-15092*(1078+7*23709^(1/2))^(1/3)-98*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+6971475+45276*23709^(1/2)-28*(1078+7*23709^(1/2))^(4/3))^(1/2))
1/18/(1078+7*23709^(1/2))^(2/3)*(-21*(1078+7*23709^(1/2))^(1/3)-3234-21*23709^(1/2)+42*(1078+7*23709^(1/2))^(2/3)-3*i*(147*(1078+7*23709^(1/2))^(2/3)-15092*(1078+7*23709^(1/2))^(1/3)-98*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+6971475+45276*23709^(1/2)-28*(1078+7*23709^(1/2))^(4/3))^(1/2))
1/36/(1078+7*23709^(1/2))^(2/3)*(-3234*i*3^(1/2)+21*i*(1078+7*23709^(1/2))^(1/3)*3^(1/2)-21*i*3^(1/2)*23709^(1/2)+21*(1078+7*23709^(1/2))^(1/3)+84*(1078+7*23709^(1/2))^(2/3)+3234+21*23709^(1/2)+3*(90552*i*3^(1/2)*23709^(1/2)+13942950*i*3^(1/2)+13942950+294*(1078+7*23709^(1/2))^(2/3)-294*i*3^(1/2)*(1078+7*23709^(1/2))^(2/3)+90552*23709^(1/2)+60368*(1078+7*23709^(1/2))^(1/3)+392*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+112*(1078+7*23709^(1/2))^(4/3))^(1/2))
1/36/(1078+7*23709^(1/2))^(2/3)*(-3234*i*3^(1/2)+21*i*(1078+7*23709^(1/2))^(1/3)*3^(1/2)-21*i*3^(1/2)*23709^(1/2)+21*(1078+7*23709^(1/2))^(1/3)+84*(1078+7*23709^(1/2))^(2/3)+3234+21*23709^(1/2)-3*(90552*i*3^(1/2)*23709^(1/2)+13942950*i*3^(1/2)+13942950+294*(1078+7*23709^(1/2))^(2/3)-294*i*3^(1/2)*(1078+7*23709^(1/2))^(2/3)+90552*23709^(1/2)+60368*(1078+7*23709^(1/2))^(1/3)+392*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+112*(1078+7*23709^(1/2))^(4/3))^(1/2))
1/36/(1078+7*23709^(1/2))^(2/3)*(3234*i*3^(1/2)-21*i*(1078+7*23709^(1/2))^(1/3)*3^(1/2)+21*i*3^(1/2)*23709^(1/2)+21*(1078+7*23709^(1/2))^(1/3)+84*(1078+7*23709^(1/2))^(2/3)+3234+21*23709^(1/2)+3*(-90552*i*3^(1/2)*23709^(1/2)-13942950*i*3^(1/2)+13942950+294*(1078+7*23709^(1/2))^(2/3)+294*i*3^(1/2)*(1078+7*23709^(1/2))^(2/3)+90552*23709^(1/2)+60368*(1078+7*23709^(1/2))^(1/3)+392*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+112*(1078+7*23709^(1/2))^(4/3))^(1/2))
1/36/(1078+7*23709^(1/2))^(2/3)*(3234*i*3^(1/2)-21*i*(1078+7*23709^(1/2))^(1/3)*3^(1/2)+21*i*3^(1/2)*23709^(1/2)+21*(1078+7*23709^(1/2))^(1/3)+84*(1078+7*23709^(1/2))^(2/3)+3234+21*23709^(1/2)-3*(-90552*i*3^(1/2)*23709^(1/2)-13942950*i*3^(1/2)+13942950+294*(1078+7*23709^(1/2))^(2/3)+294*i*3^(1/2)*(1078+7*23709^(1/2))^(2/3)+90552*23709^(1/2)+60368*(1078+7*23709^(1/2))^(1/3)+392*(1078+7*23709^(1/2))^(1/3)*23709^(1/2)+112*(1078+7*23709^(1/2))^(4/3))^(1/2))

>>

网友（2）：

x+y=7-z,y+z=7-x,x+z=7-y
(X+Y)(Y+Z)(Z+X)=(7-x)(7-y)(7-z)
=343-49(x+y+z)+7(xy+xz+yz)-xyz
=343-49*7+7*14+8
=106