Question

已知x+y+z=0,x+2y-8z=0,那么（2x+3y+5z）/(x+2y+z)=

Answer 1

① x+y+z=0
②x+2y-8z=0
(2x+3y+5z)/(x+2y+z)
=(y+3z)/y
②-①y=9z
所以原式：
12z/9z
=12/9
=4/3

Answer 2

x+y+z=0
x+2y-8z=0
第一种x y都用Z代替
即：（x+2y-8z）-（x+y+z）=0
y-9z=0
y=9z
x+y+z=x+9z+z=0
x=-10z
（2x+3y+5z）/(x+2y+z)=[2*(-10z)+3*9z+5z]/[-10z+2*9z+z]=12z/9z=12/9

第二种：
x+2y-8z=0即x+2y+z=9z
（x+2y-8z）+（x+y+z）=0即2x+3y-7z=0即2x+3y+5z=12z
2x+3y+5z）/(x+2y+z)=12z/9z=12/9