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so dear community, here is my second question.

assume we have a system, where

$A_1 x + B_1 y = C_1 $

$A_2 x^2 + B_2 y^2 = C_2 $

$A_3 x^3 + B_3 y^3 = C_3 $

etc.

can this system be solved?

if yes, i would appreciate some guidance.

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closed as too localized by Bill Johnson, Andy Putman, Felipe Voloch, Zev Chonoles, Andres Caicedo Dec 4 2011 at 17:52

1 Answer

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The first two equations determine your $x, y$ up to finite indeterminacy, so your system is generally overdetermined. To solve the first two equations, the quadratic formula works well.

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the quadretic formula works only upto degree 2, if i am correct. what happens if the system is like $A_1 x + B_1 y + ... + Z_1 z$ $A_2 x^2 + B_2 y^2 + ... + Z_2 z^2$ $A_m x^m + B_m y^m + ... + Z_m z^m$ i.e. what happens if there is a system n variables and up to degree m ? comment . please do not misunderstand me, but would anyone ask a question in mathoverflow, if that was solvable by just quadratic formula. would they not just go to yahoo clever? also, although i used only up to degree 2 in the example, i was looking for a general way to solve this type of equations. – Sean Dec 4 2011 at 18:12
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 @Sean: Ask the question you want answered. If you cannot use proper mathematical notation, MO is not for you. Finally, look up Newton's identities. – Felipe Voloch Dec 4 2011 at 18:35
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 @Felipe: that will teach me to not just close it... – Igor Rivin Dec 4 2011 at 18:59

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