Question

已知x/(y+z)=y/(x+z)=z/(x+y)，求(x+y)/z的值。

这是在相似形中的比例线段遇到的问题，麻烦过程写详细些，谢谢！

Answer 1

上面都错! 有两种情况!

利用等比定理:

当x+y+z不等于0

x/(y+z)=y/(x+z)=z/(x+y)=(x+y+z)/(y+z+x+y+x+y)=1/2

(x+y)/z=2

当x+y+z=0

(x+y)/z=-z/z=-1

Answer 2

设x/(y+z)=y/(x+z)=z/(x+y)=k
x=yk+zk
y=xk+zk
z=xk+yk
三式相加
x+y+z=2k(x+y+z)
2k=1
k=1/2

z=1/2(x+y)
(x+y)/z
=(x+y)/[1/2(x+y)]
=2

Answer 3

x/(y+z)=y/(x+z)=z/(x+y)=(x+y+z)/[(y+z)+(x+z)+(x+y)]=1/2,
倒过来得(x+y)/z=2

Answer 4

可以表达为xy+xz=yx+yz=zx+zy xy+xz=yz+xz xy+xz=xy+yz xy+yz=xz+yz
: xy=xz=yz y=z=x 嘿嘿所以(x+y)/z=2x/x=2y/y=2z/z=2看明白了吗？

Answer 5

由等比性质得：
x/(y+z)=y/(x+z)=z/(x+y)=（x+y+z)/2(x+y+z)=1/2
所以(x+y)/z=2

Answer 6

x=y=z
(x+y)/z = 2