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10
2009 Algebra #10 - Points on Cubic that Form a Rectangle
2009 Algebra #10 - Points on Cubic that Form a Rectangle
Source:
January 2, 2012
geometry
rectangle
Problem Statement
Let
f
(
x
)
=
2
x
3
ā
2
x
f(x)=2x^3-2x
f
(
x
)
=
2
x
3
ā
2
x
. For what positive values of
a
a
a
do there exist distinct
b
,
c
,
d
b,c,d
b
,
c
,
d
such that
(
a
,
f
(
a
)
)
,
(
b
,
f
(
b
)
)
,
(
c
,
f
(
c
)
)
,
(
d
,
f
(
d
)
)
(a,f(a)),(b,f(b)),(c,f(c)),(d,f(d))
(
a
,
f
(
a
))
,
(
b
,
f
(
b
))
,
(
c
,
f
(
c
))
,
(
d
,
f
(
d
))
is a rectangle?
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