已知y+z分之x=z+x分之y=x+y分之z(x+y+z≠0)求x-y+z分之x+2y+z的值
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![已知y+z分之x=z+x分之y=x+y分之z(x+y+z≠0)求x-y+z分之x+2y+z的值](/uploads/image/z/9302570-26-0.jpg?t=%E5%B7%B2%E7%9F%A5y%2Bz%E5%88%86%E4%B9%8Bx%3Dz%2Bx%E5%88%86%E4%B9%8By%3Dx%2By%E5%88%86%E4%B9%8Bz%EF%BC%88x%2By%2Bz%E2%89%A00%EF%BC%89%E6%B1%82x-y%2Bz%E5%88%86%E4%B9%8Bx%2B2y%2Bz%E7%9A%84%E5%80%BC)
已知y+z分之x=z+x分之y=x+y分之z(x+y+z≠0)求x-y+z分之x+2y+z的值
已知y+z分之x=z+x分之y=x+y分之z(x+y+z≠0)求x-y+z分之x+2y+z的值
已知y+z分之x=z+x分之y=x+y分之z(x+y+z≠0)求x-y+z分之x+2y+z的值
设:X/(Y+Z)=Y/(Z+X)=Z/(X+Y)=K
K*(Y+Z)=X
K*(Z+X)=Y
K*(X+Y)=Z
K*(Y+Z+Z+X+X+Y)=X+Y+Z
2K*(X+Y+Z)=X+Y+Z
(x+y+z≠0),K=1/2,
K*(Z+X)=Y,X+Z=2Y
x-y+z=2Y-Y=Y
x+2y+z=2Y+2Y=4Y
x-y+z分之x+2y+z=4Y/Y=4
三个数中的任意一个数,除以另外两个数之合,得数都相等,说明这三个数相等,所以X-Y+Z分之X+2Y+Z=4