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Purple Comet Problems
2017 Purple Comet Problems
27
Purple Comet 2017 HS problem 27
Purple Comet 2017 HS problem 27
Source:
March 19, 2020
algebra
min
Problem Statement
Find the minimum value of
4
(
x
2
+
y
2
+
z
2
+
w
2
)
+
(
x
y
−
7
)
2
+
(
y
z
−
7
)
2
+
(
z
w
−
7
)
2
+
(
w
x
−
7
)
2
4(x^2 + y^2 + z^2 + w^2) + (xy - 7)^2 + (yz - 7)^2 + (zw - 7)^2 + (wx - 7)^2
4
(
x
2
+
y
2
+
z
2
+
w
2
)
+
(
x
y
−
7
)
2
+
(
yz
−
7
)
2
+
(
z
w
−
7
)
2
+
(
w
x
−
7
)
2
as
x
,
y
,
z
x, y, z
x
,
y
,
z
, and
w
w
w
range over all real numbers.
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