已知; 求 xyz分之(y+z)(z+x)(x+y)的值
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已知; 求 xyz分之(y+z)(z+x)(x+y)的值
![](http://img.wesiedu.com/upload/8/0f/80f08881886a033c8e9b5b180dc01e68.jpg)
![](http://img.wesiedu.com/upload/8/0f/80f08881886a033c8e9b5b180dc01e68.jpg)
![已知; 求 xyz分之(y+z)(z+x)(x+y)的值](/uploads/image/z/16939002-66-2.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9B+%E6%B1%82+xyz%E5%88%86%E4%B9%8B%EF%BC%88y%2Bz%EF%BC%89%EF%BC%88z%2Bx%29%EF%BC%88x%2By%29%E7%9A%84%E5%80%BC)
y设(y+z)/x=(z+x)/y=(x+y)/z=k
(y+z)=kx
(z+x)=ky
(x+y)=kz
(y+z)+(z+x)+(x+y)=kx+ky+kz
2(x+y+z)=k(x+y+z)
k=2
xyz分之(y+z)(z+x)(x+y)
=2x*2y*2z/xyz
=8xyz/xyz
=8
(y+z)=kx
(z+x)=ky
(x+y)=kz
(y+z)+(z+x)+(x+y)=kx+ky+kz
2(x+y+z)=k(x+y+z)
k=2
xyz分之(y+z)(z+x)(x+y)
=2x*2y*2z/xyz
=8xyz/xyz
=8
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