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AZE JBMO TST
AZE JBMO TST
Source: AZE JBMO TST
May 2, 2015
inequalities
Problem Statement
Let
x
,
y
x,y
x
,
y
and
z
z
z
be non-negative real numbers satisfying the equation
x
+
y
+
z
=
x
y
z
x+y+z=xyz
x
+
y
+
z
=
x
yz
. Prove that
2
(
x
2
+
y
2
+
z
2
)
≥
3
(
x
+
y
+
z
)
2(x^2+y^2+z^2)\geq3(x+y+z)
2
(
x
2
+
y
2
+
z
2
)
≥
3
(
x
+
y
+
z
)
.
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