MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Other Middle and High School Contests
Math Prize For Girls Problems
2012 Math Prize For Girls Problems
8
8
Part of
2012 Math Prize For Girls Problems
Problems
(1)
Math Prize 2012 Problem 8
Source:
9/24/2012
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
?
AMC
USA(J)MO
USAMO