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Soros Olympiad in Mathematics
II Soros Olympiad 1995 - 96 (Russia)
10.2
min |a-1|+|b-2|+c-3|+|3a+2b+c| (II Soros Olympiad 1995-96 R1 10.2)
min |a-1|+|b-2|+c-3|+|3a+2b+c| (II Soros Olympiad 1995-96 R1 10.2)
Source:
June 3, 2024
algebra
inequalities
Problem Statement
Find the smallest value that the expression can take
∣
a
−
1
∣
+
∣
b
−
2
∣
+
c
−
3
∣
+
∣
3
a
+
2
b
+
c
∣
|a-1|+|b-2|+c-3|+|3a+2b+c|
∣
a
−
1∣
+
∣
b
−
2∣
+
c
−
3∣
+
∣3
a
+
2
b
+
c
∣
(
a
a
a
,
b
b
b
and
c
c
c
are arbitrary numbers).
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