已知2分之x y=3分之y z

x^2+y^2+z^2-xy-yz-xz=(1/2)[(x-y)^2+(z-y)^2+(z-x)^2]x-y=1/2+根号3z-y=1/2-根号3所以y=x-(1/2+根号3)=z-(1/2-根号3)

设x/2=y/3=z/4=a则:x=2a;y=3a;z=4a代入得：(xy+yz+zx)/(x^2+y^2+z^2)=(6a^2+12a^2+8a^2)/(4a^2+9a^2+16a^2)=26a^2

设2分之x=3分之y=4分之z=k∴x=2k,y=3k,z=4kx2+y2+z2分之xy+yz+zx=(6k²+12k²+8k²)/(4k²+9k²+

xy/(x+y)=51/x+1/y=1/5yz/(y+z)=7/21/y+1/z=2/7zx/(z+x)=41/x+1/z=1/4(xy+yz+zx)分之xyz=1/(1/x+1/y+1/z)=280

设x/2=y/3=z/4=k∴x=2k,y=3k,z=4k∴（xy+yz+zx）/（x²+y²+z²）=（6k²+12k²+8k²）/（4k

令x/3=y/4=z/5=kx=3ky=4kz=5k原式=(3k)^2+(4k)^2+(5k)^2/3k*4k+4k*5k+3k*5k=50k^2/47k^2=50/47

∵x/2=y/3=z/4∴可设x=2k;y=3k;z=4k5x的平方+3y的平方+z的平方分之xy+yz+zx=(6k²+12k²+8k²)/(20k²+27k

x/z=y/3=-2/5y=-6/5(xy+yz+zx)/z^2=(-5/6*x/z-5/6+x/z)/z=(1/3-5/6-2/5)/z=(-9/10)/z=-9/(10z)

x+y分之xy=1,y+z分之yz=2,z+x分之zx=3每个等式左右均取倒数,所以：1/x+1/y=11/y+1/z=1/21/z+1/x=1/3设：1/x=a1/y=b1/z=ca+b=1----

令3分之x=4分之y=6分之z=kx=3k,y=4kz=6k(xy+yz+xz)/(x^2+y^2+z^2)=k^2(12+18+24)/k^2(36+16+9)=54/61

由已知得(x+y)/(xy)=1(y+z)/(yz)=1/2(z+x)/(zx)=1/3变形：1/x+1/y=1(1)1/y+1/z=1/2(2)1/z+1/x=1/3(3)[(1)+(2)+(3)]

已知（xy分之x+y)的-1次方=1,则xy=x+yy=x/(x-1)（yz分之y+z)的-1次方=2,则yz=2y+2zz=2y/(y-2)（xz分之x+z)的-1次方=3,则xz=3x+3zz=3

【x+y】分之xy=-2,xy分之【x+y】=-1/21/x+1/y=-1/2(1)【y+z】分之yz=3分之4,yz分之【y+z】=3/41/y+1/z=3/4(2)【z+x】分之zx=-3分之4,

3x-4y＝z,2x+y＝8z,解得：x=3z,y=2zxy+yz分之x二次方+y二次方-z二次方=(x^2+y^2-z^2)/(xy+yz)=(9z^2+4z^2-z^2)/(6z^2+2z^2)=

答案11分之14看图

答案是11分之14. 求采纳

令a=xx=6a.y=4a.z=3a(2x^2-yz+z^2)/(x^2-2xy+z^2)=(72a^2-12a^2+9a^2)/(36a^2-48a^2+9a^2)=69a^2/(-3a^2)=-2

x分之3=y分之1x=3yy分之1=z分之2z=2yxy+yz+zx分之2x²-2y²+5z²=[2(3y)²-2y²+5(2y)²]/(3

令3/x=4/y=6/z=1/k则x=3ky=4kz=6k(x²+y²+z²)/(xy+yz+xz)=(9k²+16k²+36k²)/(12

1/x+1/y=3(1)1/y+1/z=2(2)1/x+1/z=1(3)(1)+(2)+(3)2(1/x+1/y+1/z)=61/x+1/y+1/z=3(4)由（1）1/z=0题目有误,请核对,或者更