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1989 Polish MO Finals
3
Inequality in 4 variables
Inequality in 4 variables
Source: Problem 6, Polish NO 1989
October 1, 2005
inequalities
inequalities unsolved
Problem Statement
Show that for positive reals
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
we have
(
a
b
+
a
c
+
a
d
+
b
c
+
b
d
+
c
d
6
)
3
≥
(
a
b
c
+
a
b
d
+
a
c
d
+
b
c
d
4
)
2
\left(\dfrac{ab + ac + ad + bc + bd + cd}{6} \right)^3 \geq \left(\dfrac{abc + abd + acd + bcd}{4}\right)^2
(
6
ab
+
a
c
+
a
d
+
b
c
+
b
d
+
c
d
)
3
≥
(
4
ab
c
+
ab
d
+
a
c
d
+
b
c
d
)
2
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