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Canada National Olympiad
2012 Canada National Olympiad
1
1
Part of
2012 Canada National Olympiad
Problems
(1)
Non-homogeneous xyz inequality
Source: Canadian MO 2012
5/4/2012
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
.
inequalities
induction
inequalities proposed