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Serbia JBMO TST
2024 Serbia JBMO TST
2
Symmetric 3-variable inequality
Symmetric 3-variable inequality
Source: Serbia JBMO TST 2024 P2
May 25, 2024
inequalities
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive reals such that
a
b
+
b
c
+
c
a
=
3
4
ab+bc+ca=\frac{3}{4}
ab
+
b
c
+
c
a
=
4
3
. Show that
(
a
+
b
+
c
)
6
≥
(
9
8
)
3
(
1
+
(
a
+
b
)
2
)
(
1
+
(
b
+
c
)
2
)
(
1
+
(
c
+
a
)
2
)
.
(a+b+c)^6 \geq (\frac{9} {8})^3(1+(a+b)^2)(1+(b+c)^2)(1+(c+a)^2).
(
a
+
b
+
c
)
6
≥
(
8
9
)
3
(
1
+
(
a
+
b
)
2
)
(
1
+
(
b
+
c
)
2
)
(
1
+
(
c
+
a
)
2
)
.
When does equality hold?
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