设x+y+z=3,求代数式(3(xyz-xy-xz-yz)+6)/((x-1)^3+(y-1)^3+(z-1)^3)的值

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/07/18 02:26:43

x+y+z=3,x+y+z-3=0,(x-1)+(y-1)+(z-1)=0
令 a=x-1,b=y-1,c=z-1
则 x=a+1,y=b+1,z=c+1,a+b+c=0
(3(xyz-xy-xz-yz)+6)/((x-1)^3+(y-1)^3+(z-1)^3)
=(3(xyz-xy-xz+x-yz+y-x-y)+6)/((x-1)^3+(y-1)^3+(z-1)^3)
=(3(xy(z-1)-x(z-1)-y(z-1)-(x+y))+6)/((x-1)^3+(y-1)^3+(z-1)^3)
=(3((z-1)(xy-x-y)-(x+y))+6)/((x-1)^3+(y-1)^3+(z-1)^3)
=(3((z-1)(xy-x-y+1-1)-(x+y))+6)/((x-1)^3+(y-1)^3+(z-1)^3)
=(3((z-1)(x(y-1)-(y-1)-1)-(x+y))+6)/((x-1)^3+(y-1)^3+(z-1)^3)
=(3((z-1)((y-1)(x-1)-1)-(x+y))+6)/((x-1)^3+(y-1)^3+(z-1)^3)
=(3((z-1)(y-1)(x-1)-z+1-x-y)+6)/((x-1)^3+(y-1)^3+(z-1)^3)
=(3(z-1)(y-1)(x-1)+1-(x+y+z))+6)/((x-1)^3+(y-1)^3+(z-1)^3)
=(3(z-1)(y-1)(x-1)+1-3)+6)/((x-1)^3+(y-1)^3+(z-1)^3)
=(3(z-1)(y-1)(x-1)-6+6)/((x-1)^3+(y-1)^3+(z-1)^3)
=3abc/(a^3+b^3+c^3)
=3abc/[(a+b+c)(a^2+b^2+c^2-ab-bc-ac)+3abc] … a³+b³+c³=(a+b+c)(a²+b²+c²-ab-bc-ac)+3abc
=3abc/[0*(a^2+b^2+c^2-ab-bc-ac)+3abc]
=3abc/(3abc)
=1

设x+y+z=3.求代数式[3[xyz-xy-xz-yz]+6]/[[x-1]^3+[y-1]^3+[z-1]^3]的值 x+y+z=1,x,y,z都是正数,求xy+yz+xz-3xyz的最大值和最小值 X,Y,Z为实数,且XY/X+Y=1/3,YZ/Y+Z=1/4,XZ/X+Z=1/5,求XYZ/XY+YZ+XZ的值 1/x+1/y=1/2,1/y+1/z=1/3,1/x+1/z=1/6,求xyz/(xy+yz+xz)的值 1.x,y,z为实数,且xy/x+y=1/3,yz/y+z=1/4,xz/x+z=1/5,求xyz/xy+yz+zx的值 x,y,z为实数,且xy/x+y=1/3,yz/y+z=1/4,xz/x+z=1/5,求xyz/xy+yz+zx的值急!x,y,z为实数,且xy/x+y=1/3,yz/y+z=1/4,xz/x+z=1/5,求xyz/xy+yz+zx的值 xy/x+y=1 yz/y+z=2 xz/x+z=3 求xyz/x+y+z=? 已知x+y+z=3,xy+yz+xz=-1,xyz=2,求x^2y^2+y^2z^2+x^2z^2 x-3=y-2=z-1,求x^2+y^2+z^2-xy-yz-xz的值已知xyz=1,求x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)的值已知1=xy/x+y,2=yz/y+z,3=xz/x+z,求x+y+z的值