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CIIM
2020 CIIM
5
5
Part of
2020 CIIM
Problems
(1)
2021 equations
Source: CIIM 2020 P5
10/26/2020
Determine all the positive real numbers
x
1
,
x
2
,
x
3
,
…
,
x
2021
x_1, x_2, x_3, \dots, x_{2021}
x
1
,
x
2
,
x
3
,
…
,
x
2021
such that
x
i
+
1
=
x
i
3
+
2
3
x
i
2
x_{i+1}=\frac{x_i^3+2}{3x_i^2}
x
i
+
1
=
3
x
i
2
x
i
3
+
2
for every
i
=
1
,
2
,
3
,
…
,
2020
i=1, 2, 3, \dots, 2020
i
=
1
,
2
,
3
,
…
,
2020
and
x
2021
=
x
1
x_{2021}=x_1
x
2021
=
x
1
algebra