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Problem 2
inequality, sum xy>=4sum x^2y^2+5xyz with x+y+z=1 (Serbia MO 2006 1st Grade P2)
inequality, sum xy>=4sum x^2y^2+5xyz with x+y+z=1 (Serbia MO 2006 1st Grade P2)
Source:
April 10, 2021
inequalities
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be positive numbers with
x
+
y
+
z
=
1
x+y+z=1
x
+
y
+
z
=
1
. Show that
y
z
+
z
x
+
x
y
≥
4
(
y
2
z
2
+
z
2
x
2
+
x
2
y
2
)
+
5
x
y
z
.
yz+zx+xy\ge4\left(y^2z^2+z^2x^2+x^2y^2\right)+5xyz.
yz
+
z
x
+
x
y
≥
4
(
y
2
z
2
+
z
2
x
2
+
x
2
y
2
)
+
5
x
yz
.
When does equality hold?
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