Solve a system of equations for positive (x, y, z) I arrived at the system of equations (

Sydney Stanley

Sydney Stanley

Answered question

2022-04-20

Solve a system of equations for positive (x, y, z)
I arrived at the system of equations
(3+2z)x=3(1xy)
(3+7z)y=4(1xy)
3yx+z(yx)=2xy
while working on a geometric problem, with x, y and z representing segment lengths of a quadrilateral configuration. The system is inherently quartic. Given its non-standard appearance, I am not sure yet how to rearrange the pieces, which would lead to the solutions smoothly. A math tool I have spills out ((122,133,1), without indicating how.
Before resorting to brute-force substitution, I would like to have a shot at anyone who may have expertise, or just happens to be conversant in such systems.

Answer & Explanation

morpheus1ls1

morpheus1ls1

Beginner2022-04-21Added 22 answers

All three equations of the equivalence system provided by Moo are correct and have the same collection of roots as the system posted by Quanto. As mentioned by Moo, it has 2 real roots and 2 complex roots. The two real roots are given below.
x1=12 x2=4.542124309455065516y1=13 y2=0.584929333410679641z1=1 z2=-2.04715204771556650   
Quanto has mentioned in his post that x, y and z represent segment lengths of a quadrilateral configuration, which cropped up in a problem in geometry. Therefore, I think it is safe to assume that x,y,z0. If I am right, as par as Quanto's requirement is concerned, there is only one valid set of solutions available.

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