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Contests
National and Regional Contests
Greece Contests
Greece National Olympiad
2004 Greece National Olympiad
1
1
Part of
2004 Greece National Olympiad
Problems
(1)
Best constant
Source: Greek national M.O. 2004, Final Round,problem 1
11/15/2011
Find the greatest value of
M
M
M
∈
R
\in \mathbb{R}
∈
R
such that the following inequality is true
∀
\forall
∀
x
,
y
,
z
x, y, z
x
,
y
,
z
∈
R
\in \mathbb{R}
∈
R
x
4
+
y
4
+
z
4
+
x
y
z
(
x
+
y
+
z
)
≥
M
(
x
y
+
y
z
+
z
x
)
2
x^4+y^4+z^4+xyz(x+y+z)\geq M(xy+yz+zx)^2
x
4
+
y
4
+
z
4
+
x
yz
(
x
+
y
+
z
)
≥
M
(
x
y
+
yz
+
z
x
)
2
.
inequalities
rearrangement inequality
inequalities unsolved