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Mexico Contests
Mexico National Olympiad
2011 Mexico National Olympiad
3
3
Part of
2011 Mexico National Olympiad
Problems
(1)
Quadratic system
Source: Mexico National Olympiad 2011 Problem 3
6/22/2014
Let
n
n
n
be a positive integer. Find all real solutions
(
a
1
,
a
2
,
…
,
a
n
)
(a_1, a_2, \dots, a_n)
(
a
1
,
a
2
,
…
,
a
n
)
to the system:
a
1
2
+
a
1
−
1
=
a
2
a_1^2 + a_1 - 1 = a_2
a
1
2
+
a
1
−
1
=
a
2
a
2
2
+
a
2
−
1
=
a
3
a_2^2 + a_2 - 1 = a_3
a
2
2
+
a
2
−
1
=
a
3
⋮
\hspace*{3.3em} \vdots
⋮
a
n
2
+
a
n
−
1
=
a
1
a_{n}^2 + a_n - 1 = a_1
a
n
2
+
a
n
−
1
=
a
1
quadratics
inequalities
algebra
system of equations
algebra proposed