作业帮若xy+yz+zx=0,3xyz+x^2(y+z)+y^2(z+x)+z^2(x+y)等于?
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/09 19:01:44
若xy+yz+zx=0,3xyz+x^2(y+z)+y^2(z+x)+z^2(x+y)等于?
若xy+yz+zx=0,3xyz+x^2(y+z)+y^2(z+x)+z^2(x+y)等于?
若xy+yz+zx=0,3xyz+x^2(y+z)+y^2(z+x)+z^2(x+y)等于?
将3xyz+x^2(y+z)+y^2(z+x)+z^2(x+y)拆开,得:
3XYZ+X^2Y+X^2Z+Y^2Z+Y^2Z+Y^2X+Z^2X+Z^2Y
将xy+yz+zx=0乘X 乘Y 乘Z分别得:
X^2Y+XYZ+X^2Z=0 ①
Y^2X+Y^2Z+XYZ=0 ②
XYZ+Z^2Y+Z^2X=0 ③
①+②+③恰好得3XYZ+X^2Y+X^2Z+Y^2Z+Y^2Z+Y^2X+Z^2X+Z^2Y=3xyz+x^2(y+z)+y^2(z+x)+z^2(x+y)=0
所以3xyz+x^2(y+z)+y^2(z+x)+z^2(x+y)=0
解:3xyz+x^2*(y+z)+y^2*(x+z)+z^2*(x+y)=3xyz+x^2*y+x^2z+y^2*x+y^2*z+z^2*x+z^2*y=3xyz+xy(x+y)+yz(y+z)+xz(x+z)=xyz+xy(x+y)+xyz+yz(y+z)+xyz+xz(x+z)=xy(x+y+z)+yz(x+y+z)+yz(x+y+z)=(x+y+z)(xy+yz+xz)=(x+y+z)*0=0.
xy 2yz 3zx 4xyz________ = ________ = _______ = ___________ (xyz不等于0)x+y+xy y+z+yz z+x+zx xy+yz+zx最好有解题思路 算出 X Y Z 分别等于几
XYZ满足XY/X+Y=-2,YZ/Y+Z=3/4,ZX/Z+X=-4/3,求XYZ/XY+YZ+ZX的值
分式题:xy=x+y,yz=2(y+z),zx=3(z+x),求xyz/(xy+yz+xz)xy=x+y,yz=2(y+z),zx=3(z+x),求xyz/(xy+yz+xz)
若xy+yz+zx=0,3xyz+x^2(y+z)+y^2(z+x)+z^2(x+y)等于?
+++++++若z分之x=3分之y=-5分之2 (xyz不为0) 求z的平方分之xy+yz+zx的值
若x^2y+xy^2+y^2z+yz^2+z^2x+zx^2+3xyz=k(x+y+z)*(xy+yz+zx),则k的值是
求证不等式 xyz[yz(y+z)+zx(z+x)+xy(x+y)]>=2(xy+yz+xz)^2
若x+y+z=6,xy+yz+zx=11,x^3+y^3+z^3-3xyz
数学题 xy&x+y =-2,yz&y+z=4&3 zx&z+x=-4&3 求XYZ%xy+xz+yz
XYZ满足XY/X+Y=-2,YZ/Y+Z=3/4,ZX/Z+X=-4/3,求XYZ/XY+YZ+ZX的值求快速啊
若x+y+z=6,xy+yz+zx=11,xyz=6,则x/yz+y/zx+z/xy=
若x+y+z=6,xy+yz+zx=11,xyz=6,则x/yz+y/zx+z/xy=
x+y分之xy=5,y+z分之yz=2分之7,z+x分之zx=4,则xy+yz+zx分之xyz=?
已知2分之x=3分之y=4分之z,且xyz不等于0,求分式x2+y2+z2分之xy+yz+zx的值
(x+y-xy)/(x+y+2xy)=(y+z-2yz)/(y+z+3yz)=(z+x-3zx)/(z+x+4zx),且2/x=3/y=1/z,则xyz=?
已知（x+y-xy）/(x+y+2xy)=(y+z-2yz)/(y+z+3yz)=(z+x-3zx)/(z+x+4zx),且2/x=3/y-1/z,则xyz=?
已知三个数x,y,z满足【x+y】分之xy=-2,【y+z】分之yz=3分之4,【z+x】分之zx=-3分之4,【xy+yz+zx】分之xyz=?
已知三个数x,y,z.满足xy/x十y=一2,yz/y十z=4/3,zx/z十x=一4/3则xyz/xy十yz十zx的值