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Find all x,y,z - JBMO Shortlist
Find all x,y,z - JBMO Shortlist
Source:
October 30, 2010
inequalities proposed
inequalities
Problem Statement
Find all the triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of real numbers such that
2
x
y
−
1
+
2
y
z
−
1
+
2
z
x
−
1
≥
x
y
+
y
z
+
z
x
2x\sqrt{y-1}+2y\sqrt{z-1}+2z\sqrt{x-1} \ge xy+yz+zx
2
x
y
−
1
+
2
y
z
−
1
+
2
z
x
−
1
≥
x
y
+
yz
+
z
x
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