已知非负实数a、b、c满足条件:3a+2b+c=4, 2a+b+3c=5, 设S=5a+4b+7c
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发布时间：2024-10-23 18:05
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热心网友
时间：2024-11-06 15:36
3a＋2b＋c=4 (1)
2a＋b＋3c=5 (2)
(2)*2-(1)
a+5c=6
a=6-5c
a>=0,6-5c>=0
c<=6/5
(1)*2-(2)*3
b-7c=-7
b=7c-7>=0
c>=1
所以1<=c<=6/5
S=5a+4b+7c=5(6-5c)+4(7c-7)+7c
=10c+2
1<=c<=6/5
10<=10c<=12
12<=10c+2=S<=14
所以m=14,n=12
n-m=-2
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