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2011 Canadian Students Math Olympiad
3
Canadian Students Math Olympiad 2011 Problem 3
Canadian Students Math Olympiad 2011 Problem 3
Source:
July 19, 2011
inequalities proposed
inequalities
Problem Statement
Find the largest
C
∈
R
C \in \mathbb{R}
C
∈
R
such that
x
+
z
(
x
−
z
)
2
+
x
+
w
(
x
−
w
)
2
+
y
+
z
(
y
−
z
)
2
+
y
+
w
(
y
−
w
)
2
+
∑
c
y
c
1
x
≥
C
x
+
y
+
z
+
w
\frac{x+z}{(x-z)^2} +\frac{x+w}{(x-w)^2} +\frac{y+z}{(y-z)^2}+\frac{y+w}{(y-w)^2} + \sum_{cyc} \frac{1}{x} \ge \frac{C}{x+y+z+w}
(
x
−
z
)
2
x
+
z
+
(
x
−
w
)
2
x
+
w
+
(
y
−
z
)
2
y
+
z
+
(
y
−
w
)
2
y
+
w
+
cyc
∑
x
1
≥
x
+
y
+
z
+
w
C
where
x
,
y
,
z
,
w
∈
R
+
x,y,z,w \in \mathbb{R^+}
x
,
y
,
z
,
w
∈
R
+
.Author: Hunter Spink
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