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1987 Greece Junior Math Olympiad
4
x+y+z=x^2+y^2+z^2=x^3+y^3+z^3=1 - Greece Juniors 1987 p4
x+y+z=x^2+y^2+z^2=x^3+y^3+z^3=1 - Greece Juniors 1987 p4
Source:
September 13, 2024
algebra
system of equations
Problem Statement
If
x
+
y
+
z
=
x
2
+
y
2
+
z
2
=
x
3
+
y
3
+
z
3
=
1
w
i
t
h
x
,
y
,
z
∈
R
,
x+y+z=x^2+y^2+z^2=x^3+y^3+z^3=1 \ \ with \ \ x,y,z\in \mathbb{R},
x
+
y
+
z
=
x
2
+
y
2
+
z
2
=
x
3
+
y
3
+
z
3
=
1
w
i
t
h
x
,
y
,
z
∈
R
,
prove that at least one of
x
,
y
,
z
x,y,z
x
,
y
,
z
is equal to zero.
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