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Contests
National and Regional Contests
Moldova Contests
Moldova National Olympiad
2002 Moldova National Olympiad
12.5
Integral inequality
Integral inequality
Source: MDA
December 3, 2021
inequalities
calculus
Problem Statement
Let
0
≤
a
≤
b
≤
c
≤
3
0 \le a \le b \le c \le 3
0
≤
a
≤
b
≤
c
≤
3
Prove :
(
a
−
b
)
(
a
2
−
9
)
+
(
a
−
c
)
(
b
2
−
9
)
+
(
b
−
c
)
(
c
2
−
9
)
≤
36
(a-b)(a^2-9)+(a-c)(b^2-9)+(b-c)(c^2-9) \le 36
(
a
−
b
)
(
a
2
−
9
)
+
(
a
−
c
)
(
b
2
−
9
)
+
(
b
−
c
)
(
c
2
−
9
)
≤
36
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