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7
2004 Algebra #7
2004 Algebra #7
Source:
December 26, 2011
function
Problem Statement
If
x
x
x
,
y
y
y
,
k
k
k
are positive reals such that
3
=
k
2
(
x
2
y
2
+
y
2
x
2
)
+
k
(
x
y
+
y
x
)
,
3=k^2\left(\dfrac{x^2}{y^2}+\dfrac{y^2}{x^2}\right)+k\left(\dfrac{x}{y}+\dfrac{y}{x}\right),
3
=
k
2
(
y
2
x
2
+
x
2
y
2
)
+
k
(
y
x
+
x
y
)
,
find the maximum possible value of
k
k
k
.
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