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Regional Mathematical Olympiad
2016 India Regional Mathematical Olympiad
5
Lower bound on a product
Lower bound on a product
Source: RMO Maharashtra and Goa 2016, P5
October 11, 2016
inequalities
algebra
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be non-negative real numbers such that
x
y
z
=
1
xyz=1
x
yz
=
1
. Prove that
(
x
3
+
2
y
)
(
y
3
+
2
z
)
(
z
3
+
2
x
)
≥
27.
(x^3+2y)(y^3+2z)(z^3+2x) \ge 27.
(
x
3
+
2
y
)
(
y
3
+
2
z
)
(
z
3
+
2
x
)
≥
27.
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