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2023 China Northern MO
2
China Northern Mathematical Olympiad 2023 , Problem 2
China Northern Mathematical Olympiad 2023 , Problem 2
Source: 10 Aug China
August 11, 2023
inequalities
algebra
inequalities proposed
Inequality
Problem Statement
Let
a
,
b
,
c
∈
(
0
,
1
)
a,b,c \in (0,1)
a
,
b
,
c
∈
(
0
,
1
)
and
a
b
+
b
c
+
c
a
=
4
a
b
c
.
ab+bc+ca=4abc .
ab
+
b
c
+
c
a
=
4
ab
c
.
Prove that
a
+
b
+
c
≥
1
−
a
+
1
−
b
+
1
−
c
\sqrt{a+b+c}\geq \sqrt{1-a}+\sqrt{1-b}+\sqrt{1-c}
a
+
b
+
c
≥
1
−
a
+
1
−
b
+
1
−
c
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