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France JBMO TST
2020 JBMO TST of France
4
Inequality
Inequality
Source: France JBMO TST 2020 Test 2 P4
March 11, 2020
inequalities
algebra
France
JBMO TST
Problem Statement
a
,
b
,
c
a, b, c
a
,
b
,
c
are real positive numbers for which
a
+
b
+
c
=
3
a+b+c=3
a
+
b
+
c
=
3
. Prove that
a
12
+
b
12
+
c
12
+
8
(
a
b
+
b
c
+
c
a
)
≥
27
a^{12}+b^{12}+c^{12}+8(ab+bc+ca) \geq 27
a
12
+
b
12
+
c
12
+
8
(
ab
+
b
c
+
c
a
)
≥
27
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