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Moldova Team Selection Test
2018 Moldova Team Selection Test
1
interesting problem
interesting problem
Source: Moldova TST 2018
March 9, 2018
Problem Statement
Let
x
,
y
,
z
ā
Q
x,y,z \in\mathbb{Q}
x
,
y
,
z
ā
Q
,such that
(
x
+
y
+
z
)
3
=
9
(
x
2
y
+
y
2
z
+
z
2
x
)
.
(x+y+z)^3=9(x^2y+y^2z+z^2x).
(
x
+
y
+
z
)
3
=
9
(
x
2
y
+
y
2
z
+
z
2
x
)
.
Prove that
x
=
y
=
z
x=y=z
x
=
y
=
z
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