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Contests
International Contests
IMO Longlists
1986 IMO Longlists
35
35
Part of
1986 IMO Longlists
Problems
(1)
Maximum and minimum value of |a| + |b| + |c|
Source:
8/29/2010
Establish the maximum and minimum values that the sum
∣
a
∣
+
∣
b
∣
+
∣
c
∣
|a| + |b| + |c|
∣
a
∣
+
∣
b
∣
+
∣
c
∣
can have if
a
,
b
,
c
a, b, c
a
,
b
,
c
are real numbers such that the maximum value of
∣
a
x
2
+
b
x
+
c
∣
|ax^2 + bx + c|
∣
a
x
2
+
b
x
+
c
∣
is
1
1
1
for
−
1
≤
x
≤
1.
-1 \leq x \leq 1.
−
1
≤
x
≤
1.
inequalities
triangle inequality
inequalities proposed