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EGMO TST - Moldova
2021 Moldova EGMO TST
5
2^{x^2-3y+z}+2^{y^2-3z+x}+2^{z^2-3x+y}=1,5
2^{x^2-3y+z}+2^{y^2-3z+x}+2^{z^2-3x+y}=1,5
Source: Moldova EGMO TST 2021
February 4, 2023
algebra
Problem Statement
Find all triplets
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
of real numbers that satisfy the equation
2
x
2
−
3
y
+
z
+
2
y
2
−
3
z
+
x
+
2
z
2
−
3
x
+
y
=
1
,
5.
2^{x^2-3y+z}+2^{y^2-3z+x}+2^{z^2-3x+y}=1,5.
2
x
2
−
3
y
+
z
+
2
y
2
−
3
z
+
x
+
2
z
2
−
3
x
+
y
=
1
,
5.
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