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Problem 3
sum √x>=sum xy if x+y+z=3 (Serbia MO 2005 1st Grade P3)
sum √x>=sum xy if x+y+z=3 (Serbia MO 2005 1st Grade P3)
Source:
April 11, 2021
inequalities
Inequality
Problem Statement
If
x
,
y
,
z
x,y,z
x
,
y
,
z
are nonnegative numbers with
x
+
y
+
z
=
3
x+y+z=3
x
+
y
+
z
=
3
, prove that
x
+
y
+
z
≥
x
y
+
y
z
+
x
z
.
\sqrt x+\sqrt y+\sqrt z\ge xy+yz+xz.
x
+
y
+
z
≥
x
y
+
yz
+
x
z
.
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