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2010 China Northern MO
8
China Northern Mathematical Olympiad 2010 , Problem 8
China Northern Mathematical Olympiad 2010 , Problem 8
Source:
October 2, 2014
Problem Statement
Let
x
,
y
,
z
∈
[
0
,
1
]
x,y,z \in [0,1]
x
,
y
,
z
∈
[
0
,
1
]
, and
∣
y
−
z
∣
≤
1
2
,
∣
z
−
x
∣
≤
1
2
,
∣
x
−
y
∣
≤
1
2
|y-z|\leq \frac{1}{2},|z-x|\leq \frac{1}{2},|x-y|\leq \frac{1}{2}
∣
y
−
z
∣
≤
2
1
,
∣
z
−
x
∣
≤
2
1
,
∣
x
−
y
∣
≤
2
1
. Find the maximum and minimum value of
W
=
x
+
y
+
z
−
y
z
−
z
x
−
x
y
W=x+y+z-yz-zx-xy
W
=
x
+
y
+
z
−
yz
−
z
x
−
x
y
.
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