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Solving a system of 3 nonlinear equations 
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#1
Jan2313, 01:55 PM

P: 3

a = xyz
b = xy+xz+yz c = x + y + z How do you solve x, y, and z? 


#2
Jan2313, 02:14 PM

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P: 12,099

x=cyz
b=(cyz)y + (cyz)z + yz = c(y+z)y^2zyz^2 Solve this quadratic equation for y (or z), use both in a=xyz and hope that it has a nice solution? 


#3
Jan2313, 03:07 PM

P: 3

It is not a quadratic equation. And it is not a "nice" solution.
I have determined that z^3cz^2+bza = 0. So, if we can find the roots of the cubic function, then we have z as a function of a, b, and c. Then, it should be straightforward to find x and y in terms of a, b, and c. But I forget how to find the roots of a cubic function. 


#4
Jan2313, 04:46 PM

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P: 12,099

Solving a system of 3 nonlinear equations
b= c(y+z)y^2zyz^2 is a quadratic equation in y (or z).
Solutions of a cubic equation z^3cz^2+bza = 0 looks very nice in my opinion. 


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