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This question already has an answer here:

Consider a system of equations given below:

$ p_1 + p_2 + p_3 + p_4 + p_5 = 1 $

$ x_1*p_1 + x_2*p_2 + x_3*p_3 +x_4*p_4 =0$

$ x_1^2*p_1 + x_2^2*p_2 + x_3^2*p_3 +x_4^2*p_4 =1$

$ x_1^3*p_1 + x_2^3*p_2 + x_3^3*p_3 +x_4^3*p_4 =v_1$

$ x_1^4*p_1 + x_2^4*p_2 + x_3^4*p_3 +x_4^4*p_4 =v_2$

$ x_1^5*p_1 + x_2^5*p_2 + x_3^5*p_3 +x_4^5*p_4 =v_3$

$ x_1^6*p_1 + x_2^6*p_2 + x_3^6*p_3 +x_4^6*p_4 =v_4$

$ x_1^7*p_1 + x_2^7*p_2 + x_3^7*p_3 +x_4^7*p_4 =v_5$

$ x_1^8*p_1 + x_2^8*p_2 + x_3^8*p_3 +x_4^8*p_4 =v_6$

Is there a method to solve $x_i$ and $p_i$ in terms of $v_i$?

Thank You!

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marked as duplicate by Dietrich Burde, Community Apr 22 '15 at 12:03

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  • $\begingroup$ You have nine equations and nine unknown variables. In principle there is a discrete amount of solutions. But I think there is no concrete algorithm to solve this problem. $\endgroup$ – Matthias Apr 22 '15 at 11:31

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