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2023 Tuymaada Olympiad
1
3-variable inequality for variables in [0;1]
3-variable inequality for variables in [0;1]
Source: Tuymaada 2023 Junior P1
July 7, 2023
algebra
Inequality
Tuymaada
Problem Statement
Prove that for
a
,
b
,
c
∈
[
0
;
1
]
a, b, c \in [0;1]
a
,
b
,
c
∈
[
0
;
1
]
,
(
1
−
a
)
(
1
+
a
b
)
(
1
+
a
c
)
(
1
−
a
b
c
)
≤
(
1
+
a
)
(
1
−
a
b
)
(
1
−
a
c
)
(
1
+
a
b
c
)
.
(1-a)(1+ab)(1+ac)(1-abc) \leq (1+a)(1-ab)(1-ac)(1+abc).
(
1
−
a
)
(
1
+
ab
)
(
1
+
a
c
)
(
1
−
ab
c
)
≤
(
1
+
a
)
(
1
−
ab
)
(
1
−
a
c
)
(
1
+
ab
c
)
.
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