Is there a closed-form solution to the following type of system of cubic equations? $$ x_j=\sum_{i=1}^na_{ij}x_i^3,\quad\forall\,j=1,...,n $$ Here the $a_{ij}$'s are constants, and the $x_i$'s are the variables.
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1$\begingroup$ It seems that $n=2$ is awful enough. $\endgroup$– Ng Chung TakJul 15, 2022 at 1:25
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$\begingroup$ $n=2$ actually reduces to a quartic in $x_j^2$ so technically it has closed form solutions, albeit not pretty. No such luck for $n \gt 2$ though, at least not for arbitrary $a_{ij}$. $\endgroup$– dxivJul 15, 2022 at 2:40
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