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China Northern MO
2014 China Northern MO
6
6
Part of
2014 China Northern MO
Problems
(1)
China Northern Mathematical Olympiad 2014 , Problem 6
Source: China Sijiazhuang , Aug 2014
8/12/2014
Let
x
,
y
,
z
,
w
x,y,z,w
x
,
y
,
z
,
w
be real numbers such that
x
+
2
y
+
3
z
+
4
w
=
1
x+2y+3z+4w=1
x
+
2
y
+
3
z
+
4
w
=
1
. Find the minimum of
x
2
+
y
2
+
z
2
+
w
2
+
(
x
+
y
+
z
+
w
)
2
x^2+y^2+z^2+w^2+(x+y+z+w)^2
x
2
+
y
2
+
z
2
+
w
2
+
(
x
+
y
+
z
+
w
)
2
.
inequalities
inequalities proposed