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TOT 170 1988 Spring J3 (x_3 + x_4 + x_5)^5 = 3x_1 , 5x5 system

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May 9, 2020
algebrasystem of equations

Problem Statement

Find all real solutions of the system of equations {(x3+x4+x5)5=3x1(x4+x5+x1)5=3x2(x5+x1+x2)5=3x3(x1+x2+x3)5=3x4(x2+x3+x4)5=3x5\begin{cases} (x_3 + x_4 + x_5)^5 = 3x_1 \\ (x_4 + x_5 + x_1)^5 = 3x_2\\ (x_5 + x _1 + x_2)^5 = 3x_3\\ (x_1 + x_2 + x_3)^5 = 3x_4\\ (x_2 + x_3 + x_4)^5 = 3x_5 \end{cases}
(L. Tumescu , Romania)
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