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National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1986 Swedish Mathematical Competition
4
4
Part of
1986 Swedish Mathematical Competition
Problems
(1)
x+y^2 +z^3 = 3, y+z^2 +x^3 = 3, z+x^2 +y^3 = 3
Source: 1986 Swedish Mathematical Competition p4
3/28/2021
Prove that
x
=
y
=
z
=
1
x = y = z = 1
x
=
y
=
z
=
1
is the only positive solution of the system
{
x
+
y
2
+
z
3
=
3
y
+
z
2
+
x
3
=
3
z
+
x
2
+
y
3
=
3
\left\{ \begin{array}{l} x+y^2 +z^3 = 3\\ y+z^2 +x^3 = 3\\ z+x^2 +y^3 = 3\\ \end{array} \right.
⎩
⎨
⎧
x
+
y
2
+
z
3
=
3
y
+
z
2
+
x
3
=
3
z
+
x
2
+
y
3
=
3
system of equations
System
algebra