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2017-IMOC
A3
x^3+y+z=1 and cyclic, solve over R
x^3+y+z=1 and cyclic, solve over R
Source: IMOC 2017 A3
August 12, 2021
algebra
system of equations
Problem Statement
Solve the following system of equations:
{
x
3
+
y
+
z
=
1
x
+
y
3
+
z
=
1
x
+
y
+
z
3
=
1
\begin{cases} x^3+y+z=1\\ x+y^3+z=1\\ x+y+z^3=1\end{cases}
⎩
⎨
⎧
x
3
+
y
+
z
=
1
x
+
y
3
+
z
=
1
x
+
y
+
z
3
=
1
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