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3
2017 Kosovo TST Problem 3
2017 Kosovo TST Problem 3
Source:
March 19, 2017
inequalities
algebra
Problem Statement
If
a
a
a
and
b
b
b
are positive real numbers with sum
3
3
3
, and
x
,
y
,
z
x, y, z
x
,
y
,
z
positive real numbers with product
1
1
1
, prove that :
(
a
x
+
b
)
(
a
y
+
b
)
(
a
z
+
b
)
≥
27
(ax+b)(ay+b)(az+b)\geq 27
(
a
x
+
b
)
(
a
y
+
b
)
(
a
z
+
b
)
≥
27
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