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2010 Greece Junior Math Olympiad
3
Inequality
Inequality
Source: Archimedes Junior 2010
March 17, 2020
inequalities
Problem Statement
If
a
,
b
a, b
a
,
b
are positive real numbers with sum
3
3
3
and the positive real numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
have product
1
1
1
, prove that:
(
a
x
+
b
)
(
a
y
+
b
)
(
a
z
+
b
)
≥
27
(ax + b)(ay + b)(az + b) \ge 27
(
a
x
+
b
)
(
a
y
+
b
)
(
a
z
+
b
)
≥
27
. When equality holds?
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