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3
2005 Algebra #3: Maximum Value of Symmetric Equation
2005 Algebra #3: Maximum Value of Symmetric Equation
Source:
April 29, 2013
Problem Statement
Let
x
x
x
,
y
y
y
, and
z
z
z
be distinct real numbers that sum to
0
0
0
. Find the maximum possible value of
x
y
+
y
z
+
z
x
x
2
+
y
2
+
z
2
.
\dfrac {xy+yz+zx}{x^2+y^2+z^2}.
x
2
+
y
2
+
z
2
x
y
+
yz
+
z
x
.
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