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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 $


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, Andrés E. Caicedo Dec 4 '11 at 17:52

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

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 '11 at 18:12
@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 '11 at 18:35
@Felipe: that will teach me to not just close it... – Igor Rivin Dec 4 '11 at 18:59

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