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I am facing the following problem : I have an equation which could write

$$ F(x_1(Y))-F(x_2(Y)) = 0 $$

$x_1$ and $x_2$ are the largest and smallest roots of a cubic equation; their definition involves a function $Y$ I do not know and for which I try to have a Taylor expansion at $Y=0$.

The problem is that, at $Y=0$, $x_1=x_2$ and I am stuck; no way to get anything.

Any idea and suggestion will be welcomed.

Thank you very much.

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This seems to be a mathematical question, not a Mathematica question. Am I wrong? –  Jens Jul 19 '13 at 4:08
@Jens. Yes and no. Mathematica allowed be to write explicitly the solution of the roots of the cubic equation as a function of everything (loooong formmulas). The expansion, whatever it could be, will also done using Mathematica. Then Mathematica users experience could help me (i am not a very advanced user). –  Claude Leibovici Jul 19 '13 at 4:54
This really needs a bit more description, preferably with Mathematica code. As it stands i'm not sure what you are trying to do. –  Daniel Lichtblau Jul 19 '13 at 20:04
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