X/Y+Z=Y/X+Z+1=Z/X+Y-1=X+Y+Z,求x+y+z等于多少

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X/Y+Z=Y/X+Z+1=Z/X+Y-1=X+Y+Z,求x+y+z等于多少
X/Y+Z=Y/X+Z+1=Z/X+Y-1=X+Y+Z,求x+y+z等于多少

X/Y+Z=Y/X+Z+1=Z/X+Y-1=X+Y+Z,求x+y+z等于多少
利用
a/b=c/d=e/f=(a+c+e)/(b+d+f)=(a+c)/(b+d)
X/Y+Z=Y/X+Z+1=Z/X+Y-1=X+Y+Z
(X+y+z)/(2x+2y+2z-1+1)=X+Y+Z
(x+y+z)/[2(x+y+z)]=x+y+z
x+y+z=1/2

X/Y+Z=Y/X+Z+1=Z/X+Y-1
=X+Y+Z/Y+Z+X+Z+X+Y
当
X+Y+Z/Y+Z+X+Z+X+Y=x+y+z时
1.X+Y+Z=0
2.Y+Z+X+Z+X+Y为1
x+y+z=1/2

设x/y+z=y/x+z+1=z/x+y-1=K则X=KY+KZ Y=KX+K+K Z=KX+KY-K令3个式子相加 X+Y+Z=2K（X+Y+Z）所以2K=1 K=1/2即x/y+z=y/x+z+1=z/x+y-1=1/2

已知 x/(y+z)+y/(z+x)+z/(x+y)=1求 (x*x)/(y+z)+(y*y)/(x+z)+(z*z)/(x+y)=? (x+y-z)(x-y+z)= X+Y+Z=? x/y=(x+z)/(y+z)y/z=(x+y)/(x+z) (y+z)/x=(z+x)/y=(x+y)/z求x+y-z/x+y+z的值 {x+y-z=11 y+z-x=5 z+x-y=1 {x+y-z=11,x-y-z=-5,x-y+z=1 fangchengzu:X+Z=Y 7Z=X+Y+Z X+Y+Z=14 z+=x>y?++x: 用行列式的性质证明：y+z z+x x+y x y z x+y y+z z+x =2 z x y z+x x+y y+z y z x 这个怎么证? x=y; y=z; z=x/y (x-2y+z)(x+y-2z)分之（y-x)(z-x) + (x+y-2z)(y+z-2x)分之(z-y)(x-y) + (y+z-2z)(x-2y+z)分之（x-z)(y-z)=?第三部分那个是（y+z-2x)(x-2y+z)分之（x-z)(y-z) z=x^(y/z) 偏导数已知(x+y)(x+z)=x,(y+z)(y+x)=2y,(z+x)(z+y)=3z,求x,y,z 若z分之x+y+z=y分之x-y+z=x分之-x+y+z,求xyz分之(x+y)(y+z)(z+x) 已知 (x+y-z)/z=(x-y+z)/y=(y+z-x)/x,且xyz≠0,求代数式 ((x+y)(y+z)(x+z))/xyz x分之y+z=y分之z+x=z分之x+y(x+y+z不等于0）,求x+y+z分之x+y-z 分式加减法：已知x+y/z=x+z/y=y+z/x(x+y+z≠0）,求x+y-z/x+y+z