题目内容

a
b+c
=
b
c+a
=
a+c
a+b+2c
,则a:b:c=______.
a
b+c
=
b
c+a
=
a+c
a+b+2c

a+b
a+b+2c
=
a+c
a+b+2c

∴b=c,
a
2b
=
b
b+a

1
2
a
b
=
1
1+
a
b

(
a
b
)2
+
a
b
-2=0,
解得
a
b
=1或-2.
故a:b:c=1:1:1或-2:1:1.
故答案为:1:1:1或-2:1:1.
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