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8
Math Prize 2012 Problem 8
Math Prize 2012 Problem 8
Source:
September 24, 2012
AMC
USA(J)MO
USAMO
Problem Statement
Suppose that
x
x
x
,
y
y
y
, and
z
z
z
are real numbers such that
x
+
y
+
z
=
3
x + y + z = 3
x
+
y
+
z
=
3
and
x
2
+
y
2
+
z
2
=
6
x^2 + y^2 + z^2 = 6
x
2
+
y
2
+
z
2
=
6
. What is the largest possible value of
z
z
z
?
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