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2023 JBMO Shortlist
A2
JBMO Shortlist 2023 A2
JBMO Shortlist 2023 A2
Source: JBMO Shortlist 2023, A2
June 28, 2024
Inequality
JBMO
JBMO Shortlist
algebra
inequalities proposed
Problem Statement
For positive real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
with
x
y
+
y
z
+
z
x
=
1
xy+yz+zx=1
x
y
+
yz
+
z
x
=
1
, prove that
2
x
y
z
+
9
x
y
z
≥
7
(
x
+
y
+
z
)
\frac{2}{xyz}+9xyz \geq 7(x+y+z)
x
yz
2
+
9
x
yz
≥
7
(
x
+
y
+
z
)
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