MathDB
Problems
Contests
International Contests
Austrian-Polish
2000 Austrian-Polish Competition
3
3
Part of
2000 Austrian-Polish Competition
Problems
(1)
x_{n-1}^3 = x_n+ x_1 + 1, nxn system
Source: Austrian - Polish 2000 APMC
5/4/2020
For each integer
n
≥
3
n \ge 3
n
≥
3
solve in real numbers the system of equations:
{
x
1
3
=
x
2
+
x
3
+
1
.
.
.
x
n
−
1
3
=
x
n
+
x
1
+
1
x
n
3
=
x
1
+
x
2
+
1
\begin{cases} x_1^3 = x_2 + x_3 + 1 \\...\\x_{n-1}^3 = x_n+ x_1 + 1\\x_{n}^3 = x_1+ x_2 + 1 \end{cases}
⎩
⎨
⎧
x
1
3
=
x
2
+
x
3
+
1
...
x
n
−
1
3
=
x
n
+
x
1
+
1
x
n
3
=
x
1
+
x
2
+
1
algebra
system of equations