Hi,

I'm currently studying percolation theory and here I'm stuck on the this "simple" algebraic equation

[tex]ax^{n-1} - x +1 - a = 0[/tex]

clearly, the trivial solution x = 1 solves it. But I'm told that

[tex]x = 1 - \frac{2a(n-1)-2}{a(n-2)(n-1)}[/tex]

is another solution. This makes we wonder, if the equation can be put into a simpler form (e.g. quadratic or cubic) — even though I haven't succeed to.

Can any of you help ??

Thaks in advance.

I'm currently studying percolation theory and here I'm stuck on the this "simple" algebraic equation

[tex]ax^{n-1} - x +1 - a = 0[/tex]

clearly, the trivial solution x = 1 solves it. But I'm told that

[tex]x = 1 - \frac{2a(n-1)-2}{a(n-2)(n-1)}[/tex]

is another solution. This makes we wonder, if the equation can be put into a simpler form (e.g. quadratic or cubic) — even though I haven't succeed to.

Can any of you help ??

Thaks in advance.

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