Home Competitions AT-OEMO-FED1 2008 Problem 2
AT-OEMO-FED1 2008 Problem 2
Given a ∈ R + a \in R^{+} a ∈ R + n > 4 n > 4 n > 4 x 1 , . . . , x n x_1, ...,x_n x 1 , ... , x n { x 1 x 2 ( 3 a − 2 x 3 ) = a 3 x 2 x 3 ( 3 a − 2 x 4 ) = a 3 . . . x n − 2 x n − 1 ( 3 a − 2 x n ) = a 3 x n − 1 x n ( 3 a − 2 x 1 ) = a 3 x n x 1 ( 3 a − 2 x 2 ) = a 3 \begin {cases} x_1x_2(3a-2x_3) = a^3\\
x_2x_3(3a-2x_4) = a^3\\
...\\
x_{n-2}x_{n-1}(3a-2x_n) = a^3\\
x_{n-1}x_n(3a-2x_1) = a^3 \\
x_nx_1(3a-2x_2) = a^3 \end {cases} ⎩ ⎨ ⎧ x 1 x 2 ( 3 a − 2 x 3 ) = a 3 x 2 x 3 ( 3 a − 2 x 4 ) = a 3 ... x n − 2 x n − 1 ( 3 a − 2 x n ) = a 3 x n − 1 x n ( 3 a − 2 x 1 ) = a 3 x n x 1 ( 3 a − 2 x 2 ) = a 3
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