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National and Regional Contests
North Macedonia Contests
JBMO TST - Macedonia
2015 FYROM JBMO Team Selection Test
3
Inequality
Inequality
Source: 2015 JBMO TST - Macedonia, Problem 3
December 31, 2015
inequalities
3-variable inequality
Problem Statement
Let
a
,
b
a, b
a
,
b
and
c
c
c
be positive real numbers. Prove that
∏
c
y
c
(
16
a
2
+
8
b
+
17
)
≥
2
12
∏
c
y
c
(
a
+
1
)
\prod_{cyc}(16a^2+8b+17)\geq2^{12}\prod_{cyc}(a+1)
∏
cyc
(
16
a
2
+
8
b
+
17
)
≥
2
12
∏
cyc
(
a
+
1
)
.
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