MathDB
Problems
Contests
International Contests
Austrian-Polish
1999 Austrian-Polish Competition
6
6
Part of
1999 Austrian-Polish Competition
Problems
(1)
x_n^2 + x_nx_{n-1} + x_{n-1}^4 = 1 for n = 1,2,..., 1999, x_0 = x_{1999}.
Source: Austrian - Polish 1999 APMC
5/4/2020
Solve in the nonnegative real numbers the system of equations
{
x
n
2
+
x
n
x
n
−
1
+
x
n
−
1
4
=
1
f
o
r
n
=
1
,
2
,
.
.
.
,
1999
x
0
=
x
1999
\begin{cases} x_n^2 + x_nx_{n-1} + x_{n-1}^4 = 1 \,\,\,\, for \,\,\,\, n = 1,2,..., 1999 \\\ x_0 = x_{1999} \end{cases}
{
x
n
2
+
x
n
x
n
−
1
+
x
n
−
1
4
=
1
f
or
n
=
1
,
2
,
...
,
1999
x
0
=
x
1999
algebra
system of equations