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Korea Winter Program Practice Test
2016 Korea Winter Program Practice Test
4
Strange Inequality
Strange Inequality
Source: 2016 Korea Winter Camp 2nd Test #4
January 25, 2016
inequalities
Problem Statement
Let
x
,
y
,
z
≥
0
x,y,z \ge 0
x
,
y
,
z
≥
0
be real numbers such that
(
x
+
y
−
1
)
2
+
(
y
+
z
−
1
)
2
+
(
z
+
x
−
1
)
2
=
27
(x+y-1)^2+(y+z-1)^2+(z+x-1)^2=27
(
x
+
y
−
1
)
2
+
(
y
+
z
−
1
)
2
+
(
z
+
x
−
1
)
2
=
27
.Find the maximum and minimum of
x
4
+
y
4
+
z
4
x^4+y^4+z^4
x
4
+
y
4
+
z
4
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