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National and Regional Contests
Canada Contests
Canada National Olympiad
2009 Canada National Olympiad
3
3
Part of
2009 Canada National Olympiad
Problems
(1)
Determine the range
Source: Canadian Mathematical Olympiad - 2009 - Problem 3.
5/4/2011
Define
f
(
x
,
y
,
z
)
=
(
x
y
+
y
z
+
z
x
)
(
x
+
y
+
z
)
(
x
+
y
)
(
y
+
z
)
(
z
+
x
)
f(x,y,z)=\frac{(xy+yz+zx)(x+y+z)}{(x+y)(y+z)(z+x)}
f
(
x
,
y
,
z
)
=
(
x
+
y
)
(
y
+
z
)
(
z
+
x
)
(
x
y
+
yz
+
z
x
)
(
x
+
y
+
z
)
. Determine the set of real numbers
r
r
r
for which there exists a triplet of positive real numbers satisfying
f
(
x
,
y
,
z
)
=
r
f(x,y,z)=r
f
(
x
,
y
,
z
)
=
r
.
calculus
inequalities proposed
inequalities