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2009 JBMO Shortlist
5
Just Hölder
Just Hölder
Source: JBMO Shortlist 2009
May 12, 2016
Inequality
algebra
Problem Statement
A5
\boxed{\text{A5}}
A5
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be positive reals. Prove that
(
x
2
+
y
+
1
)
(
x
2
+
z
+
1
)
(
y
2
+
x
+
1
)
(
y
2
+
z
+
1
)
(
z
2
+
x
+
1
)
(
z
2
+
y
+
1
)
≥
(
x
+
y
+
z
)
6
(x^2+y+1)(x^2+z+1)(y^2+x+1)(y^2+z+1)(z^2+x+1)(z^2+y+1)\geq (x+y+z)^6
(
x
2
+
y
+
1
)
(
x
2
+
z
+
1
)
(
y
2
+
x
+
1
)
(
y
2
+
z
+
1
)
(
z
2
+
x
+
1
)
(
z
2
+
y
+
1
)
≥
(
x
+
y
+
z
)
6
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