问题 填空题
已知
a+2b-3c
2
=
b-2c+3c
3
=
c+3a+2b
4
,则
a-2b+3c
a+3b-2c
=______.(a≠0)
答案

a+2b-3c
2
=λ,则

a+2b-3c=2λ,

b-2c+3a=3λ,

c+3a+2b=4λ,

解得a=

9
11
λ,b=
8
11
λ,c=
1
11
λ,λ≠0,令μ=
1
11
λ,

a-2b+3c
a+3b-2c
=
(9-16+3)μ
(9+24-2)μ
=-
4
31

故答案为:-

4
31

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