Nonlinear Equations with Four Variables: Solving for All Solutions

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The discussion focuses on solving a system of nonlinear equations involving four variables: a, b, c, and d. Initial attempts at substitution lead to complex cubic and sixth-order equations, suggesting a more straightforward method may exist. Mathematica provides six solutions, including two real and four complex, indicating the problem's complexity. Participants express a desire to uncover a simpler solution, as the equations are presented in a high school textbook. The conversation highlights the challenge of solving nonlinear systems while seeking effective strategies.
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Homework Statement


Find all solutions of:

a + c = 5
b + d + ac = 5
ad+ bc = 5
bd = -6

Homework Equations

The Attempt at a Solution


I tried subsitution and end up with a cubic equations. I am pretty sure it can be done easier.
 
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Why do you think it can be done more simply? I got a 6th order equation. Mathematica came up with 6 solutions, two real and 4 complex. Try showing us your work.
 
Because this is written in a high school book. So there must be something we are overlooking.
 
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