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2012 Canada National Olympiad
1
Non-homogeneous xyz inequality
Non-homogeneous xyz inequality
Source: Canadian MO 2012
May 4, 2012
inequalities
induction
inequalities proposed
Problem Statement
Let
x
,
y
x,y
x
,
y
and
z
z
z
be positive real numbers. Show that
x
2
+
x
y
2
+
x
y
z
2
≥
4
x
y
z
−
4
x^2+xy^2+xyz^2\ge 4xyz-4
x
2
+
x
y
2
+
x
y
z
2
≥
4
x
yz
−
4
.
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