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Morocco National Olympiad
2011 Morocco National Olympiad
2
Equation of 5th degree
Equation of 5th degree
Source:
April 24, 2011
algebra unsolved
algebra
Problem Statement
Solve in
R
\mathbb{R}
R
the equation :
(
x
+
1
)
5
+
(
x
+
1
)
4
(
x
−
1
)
+
(
x
+
1
)
3
(
x
−
1
)
2
+
(x+1)^5 + (x+1)^4(x-1) + (x+1)^3(x-1)^2 +
(
x
+
1
)
5
+
(
x
+
1
)
4
(
x
−
1
)
+
(
x
+
1
)
3
(
x
−
1
)
2
+
(
x
+
1
)
2
(
x
−
1
)
3
+
(
x
+
1
)
(
x
−
1
)
4
+
(
x
−
1
)
5
=
(x+1)^2(x-1)^3 + (x+1)(x-1)^4 + (x-1)^5 =
(
x
+
1
)
2
(
x
−
1
)
3
+
(
x
+
1
)
(
x
−
1
)
4
+
(
x
−
1
)
5
=
0
0
0
.
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