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On reducing degree-$12$ equations with Mathieu group $M_{11}$ to its degree-$11$ resolvent?
The general $4$-deg and some $8$-deg (such as the Schein octic) when a linear transformation is done so their $x^{n-1}$ term vanishes can have a neat solution as,
$$x = \sqrt{z_1}+\sqrt{z_2}+\sqrt{z_3}...
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