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2
2017 T2: Quirky Manipulation
2017 T2: Quirky Manipulation
Source:
January 29, 2017
2017
team
Problem Statement
Suppose
x
x
x
,
y
y
y
, and
z
z
z
are nonzero complex numbers such that
(
x
+
y
+
z
)
(
x
2
+
y
2
+
z
2
)
=
x
3
+
y
3
+
z
3
(x+y+z)(x^2+y^2+z^2)=x^3+y^3+z^3
(
x
+
y
+
z
)
(
x
2
+
y
2
+
z
2
)
=
x
3
+
y
3
+
z
3
. Compute
(
x
+
y
+
z
)
(
1
x
+
1
y
+
1
z
)
.
(x+y+z)\left(\dfrac1x+\dfrac1y+\dfrac1z\right).
(
x
+
y
+
z
)
(
x
1
+
y
1
+
z
1
)
.
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