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National and Regional Contests
Bosnia Herzegovina Contests
Bosnia and Herzegovina EGMO Team Selection Test
2019 Bosnia and Herzegovina EGMO TST
1
1
Part of
2019 Bosnia and Herzegovina EGMO TST
Problems
(1)
x_k+x_{k+1}=x^2_{k+2} , n x n system
Source: Bosnia and Herzegovina EGMO TST 2019 p1
10/7/2022
Let
x
1
,
x
2
,
.
.
.
,
x
n
x_1,x_2, ..., x_n
x
1
,
x
2
,
...
,
x
n
be non-negative real numbers. Solve the system of equations:
x
k
+
x
k
+
1
=
x
k
+
2
2
,
(
k
=
1
,
2
,
.
.
.
,
n
)
,
x_k+x_{k+1}=x^2_{k+2}\,\,,\,\,\, (k =1,2,...,n),
x
k
+
x
k
+
1
=
x
k
+
2
2
,
(
k
=
1
,
2
,
...
,
n
)
,
where
x
n
+
1
=
x
1
x_{n+1} = x_1
x
n
+
1
=
x
1
,
x
n
+
2
=
x
2
x_{n+2} = x_2
x
n
+
2
=
x
2
.
algebra
system of equations