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2021 USMCA
23
2021 USMCA National Championship #23
2021 USMCA National Championship #23
Source:
May 9, 2021
Problem Statement
Given real numbers
x
,
y
,
z
,
w
x, y, z, w
x
,
y
,
z
,
w
such that
(
x
+
y
+
2
z
)
(
x
+
z
+
3
w
)
=
1
(x + y + 2z)(x + z + 3w) = 1
(
x
+
y
+
2
z
)
(
x
+
z
+
3
w
)
=
1
, what is the minimum possible value of
x
2
+
y
2
+
z
2
+
w
2
x^2 + y^2 + z^2 + w^2
x
2
+
y
2
+
z
2
+
w
2
?
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