Question

求解一道初二数学题(急!!!!!)

若x/(y+z)=y/(x+z)=z/(x+y)=k,则k的值为( )
A.0 B.1/2 C.-1 D.1/2或-1

Answer 1

B，解：因为x/(y+z)=y/(x+z)=z/(x+y)=k
所以x/(y+z)+1=y/(x+z)+1=z/(x+y)+1=k+1
所以x+y+z/(y+z)=x+y+z/(x+z)=x+y+z/(x+y)=k+1
所以1/(y+z)=1/(x+z)=1/(x+y)
所以y+z=x+z=x+y
所以x=y=z
所以k=1/2

Answer 2

学弟，教你个好办法，因为是选择题，所以代一下就OK.令X＝Y=Z＝1，就得出答案了。做题要灵活，记住了。祝，加油啊。你学习顺利

Answer 3

选B，要做这道题要懂得运用合比定理。x/(y+z)=y/(x+z)=z/(x+y)=(x+y+z)/2(x+y+z)=1/2

Answer 4

D.1/2或-1
当x+y=-z即可使k=-1
例如x=1,y=1,z=-2
k=1/2也有可能，如x=y=z但不等于0时

Answer 5

x/(y+z)=y/(x+z)=z/(x+y)=k→(x+y+z)/(2x+2y+2z)=k→1/2=k→k=1/2
这里用了等比定理