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Problems
Contests
National and Regional Contests
Vietnam Contests
Vietnam Team Selection Test
2021 Vietnam TST
4
Inequality
Inequality
Source: Vietnam TST 2021 P4-Day 2
April 2, 2021
inequalities
algebra
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
are non-negative numbers such that
2
(
a
2
+
b
2
+
c
2
)
+
3
(
a
b
+
b
c
+
c
a
)
=
5
(
a
+
b
+
c
)
2(a^2+b^2+c^2)+3(ab+bc+ca)=5(a+b+c)
2
(
a
2
+
b
2
+
c
2
)
+
3
(
ab
+
b
c
+
c
a
)
=
5
(
a
+
b
+
c
)
then prove that
4
(
a
2
+
b
2
+
c
2
)
+
2
(
a
b
+
b
c
+
c
a
)
+
7
a
b
c
≤
25
4(a^2+b^2+c^2)+2(ab+bc+ca)+7abc\le 25
4
(
a
2
+
b
2
+
c
2
)
+
2
(
ab
+
b
c
+
c
a
)
+
7
ab
c
≤
25
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