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National and Regional Contests
Turkey Contests
JBMO TST - Turkey
2016 JBMO TST - Turkey
6
An inequality with a condition
An inequality with a condition
Source: Turkey JBMO TST 2016 P6
May 22, 2016
inequalities
Problem Statement
Prove that
(
x
4
+
y
)
(
y
4
+
z
)
(
z
4
+
x
)
≥
(
x
+
y
2
)
(
y
+
z
2
)
(
z
+
x
2
)
(x^4+y)(y^4+z)(z^4+x) \geq (x+y^2)(y+z^2)(z+x^2)
(
x
4
+
y
)
(
y
4
+
z
)
(
z
4
+
x
)
≥
(
x
+
y
2
)
(
y
+
z
2
)
(
z
+
x
2
)
for all positive real numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
satisfying
x
y
z
≥
1
xyz \geq 1
x
yz
≥
1
.
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