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Austrian-Polish
1990 Austrian-Polish Competition
3
x + y^2 + z^4 = 0 , y + z^2 + x^4 = 0 , z + x^2 + y^5 = 0
x + y^2 + z^4 = 0 , y + z^2 + x^4 = 0 , z + x^2 + y^5 = 0
Source: Austrian - Polish 1990 APMC
May 7, 2020
algebra
system of equations
Problem Statement
Show that there are two real solutions to:
{
x
+
y
2
+
z
4
=
0
y
+
z
2
+
x
4
=
0
z
+
x
2
+
y
5
=
0
\begin{cases} x + y^2 + z^4 = 0 \\ y + z^2 + x^4 = 0 \\ z + x^2 + y^5 = 0\end {cases}
⎩
⎨
⎧
x
+
y
2
+
z
4
=
0
y
+
z
2
+
x
4
=
0
z
+
x
2
+
y
5
=
0
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