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1979 IMO Longlists
59
Simple old inequality - find minimum
Simple old inequality - find minimum
Source: ILL 1979 - Problem 59.
June 5, 2011
inequalities
inequalities proposed
Problem Statement
Determine the maximum value of
x
2
y
2
z
2
w
x^2 y^2 z^2 w
x
2
y
2
z
2
w
for
{
x
,
y
,
z
,
w
}
∈
R
+
∪
{
0
}
\{x,y,z,w\}\in\mathbb{R}^{+} \cup\{0\}
{
x
,
y
,
z
,
w
}
∈
R
+
∪
{
0
}
and
2
x
+
x
y
+
z
+
y
z
w
=
1
2x+xy+z+yzw=1
2
x
+
x
y
+
z
+
yz
w
=
1
.
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