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I have a set of quadratic equations of the form:

\begin{equation*} 2S_0q_0(q_0S_0 + q_1S_1 + ...... + q_iS_n)+k_0 = 0 \\ 2S_1q_1(q_0S_0 + q_1S_1 + ...... + q_iS_n)+k_1 = 0 \\ \vdots \\ 2S_nq_n(q_0S_0 + q_1S_1 + ...... + q_nS_n)+k_n = 0 \\ \end{equation*}

We have $n$ equations and $n$ variables $q_0,q_1,q_2.....q_n$. The $k$ and $S$ values are constants.

How can I analytically reach a solution for this system?

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    This is unclear; are $S_0(q_0)$, $S_1(q_1)$, etc., values of functions evaluated at $q_0$, $q_1$, etc., or is that meant to be a product of the cosntant $S_0$ and the constant $q_0$, etc.? Also, don't use asterisks for products; use juxtaposition.2010-11-04
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    Where are the equal signs?2010-11-04
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    Sorry. Had to edit it a few times. Would love to have math preview of the question while asking it.2010-11-04
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    Do you mean $q_n S_n$ (instead of $q_i S_n$) at the end of the parenthesized sums in the first two equations?2010-11-04

1 Answers 1

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Hint:

Set $X = q_0S_0 + q_1S_1 + \dots + q_n S_n$ and add up all the equations.

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    Thanks. I should have seen that !!!2010-11-04