Indetermined system <munderover> &#x2211;<!-- ∑ --> i = 1

Aedan Gonzales 2022-05-12 Answered
Indetermined system
i = 1 N x i = i = 1 N 1 x i = 3
for N > 2. The main aspect that confuses me is the general N and I'm not sure how to proceed.
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Answers (2)

Semaj Stark
Answered 2022-05-13 Author has 17 answers
Note that x + 1 x 2 if x is positive. If you add the two equations there are no solutions for N > 3 and all x i = 1 is the only solution for N = 3 unless negative values are allowed for x. If negative values are allowed you can't say much.
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Elle Weber
Answered 2022-05-14 Author has 1 answers
By Vieta's formulas the solutions of this system are the families of roots of polynomials
x n + a 1 x n 1 + + a n = 0 ,
where a 1 = 3 and a n 1 / a n = 3. Taking arbitrarily coefficients a 2 , , a n 1 , you will get all solutions.
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