MathDB
Problems
Contests
International Contests
Tournament Of Towns
1988 Tournament Of Towns
(170) 3
(170) 3
Part of
1988 Tournament Of Towns
Problems
(1)
TOT 170 1988 Spring J3 (x_3 + x_4 + x_5)^5 = 3x_1 , 5x5 system
Source:
5/9/2020
Find all real solutions of the system of equations
{
(
x
3
+
x
4
+
x
5
)
5
=
3
x
1
(
x
4
+
x
5
+
x
1
)
5
=
3
x
2
(
x
5
+
x
1
+
x
2
)
5
=
3
x
3
(
x
1
+
x
2
+
x
3
)
5
=
3
x
4
(
x
2
+
x
3
+
x
4
)
5
=
3
x
5
\begin{cases} (x_3 + x_4 + x_5)^5 = 3x_1 \\ (x_4 + x_5 + x_1)^5 = 3x_2\\ (x_5 + x _1 + x_2)^5 = 3x_3\\ (x_1 + x_2 + x_3)^5 = 3x_4\\ (x_2 + x_3 + x_4)^5 = 3x_5 \end{cases}
⎩
⎨
⎧
(
x
3
+
x
4
+
x
5
)
5
=
3
x
1
(
x
4
+
x
5
+
x
1
)
5
=
3
x
2
(
x
5
+
x
1
+
x
2
)
5
=
3
x
3
(
x
1
+
x
2
+
x
3
)
5
=
3
x
4
(
x
2
+
x
3
+
x
4
)
5
=
3
x
5
(L. Tumescu , Romania)
algebra
system of equations