Nonlinear Equations with Four Variables: Solving for All Solutions

  • Thread starter Thread starter dirk_mec1
  • Start date Start date
  • Tags Tags
    Nonlinear System
Click For Summary
SUMMARY

The discussion focuses on solving a system of nonlinear equations with four variables: a + c = 5, b + d + ac = 5, ad + bc = 5, and bd = -6. Participants explored various methods, including substitution, which led to a cubic equation and a sixth-order equation. Mathematica was utilized to find six solutions, comprising two real and four complex solutions. The conversation emphasizes the need for a simpler approach, as the problem is presented in a high school textbook.

PREREQUISITES
  • Understanding of nonlinear equations and systems of equations
  • Familiarity with substitution methods in algebra
  • Basic knowledge of complex numbers and their properties
  • Experience with Mathematica for computational assistance
NEXT STEPS
  • Research methods for solving nonlinear equations with multiple variables
  • Learn about the use of Mathematica for algebraic problem-solving
  • Explore techniques for simplifying complex algebraic expressions
  • Study the properties and applications of cubic and higher-order equations
USEFUL FOR

Students, educators, and mathematicians interested in solving complex algebraic problems, particularly those involving nonlinear equations and computational tools like Mathematica.

dirk_mec1
Messages
755
Reaction score
13

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.
 
Physics news on Phys.org
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.
 

Similar threads

  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
8
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
2
Views
2K
  • · Replies 28 ·
Replies
28
Views
2K
  • · Replies 21 ·
Replies
21
Views
2K
Replies
2
Views
2K
  • · Replies 14 ·
Replies
14
Views
3K