Solving 2 equation with 2 variables (hard)

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Homework Help Overview

The discussion revolves around solving a system of two equations with two variables, where the original poster seeks exact solutions without the use of programming tools. The problem has been characterized as challenging, particularly due to the presence of trigonometric components in the solutions.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore various methods for solving the equations, including transforming one equation into a cubic form and discussing strategies for finding roots. There is also a focus on eliminating trigonometric components from the solutions.

Discussion Status

The discussion is ongoing, with participants offering different perspectives on the problem. Some guidance has been provided regarding potential strategies for finding roots, but there is no explicit consensus on the best approach to eliminate trigonometric components.

Contextual Notes

Participants note that the problem requires exact values and that the use of programs is not permitted. There is also mention of a potential typo in the equations that could affect the solutions.

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[PLAIN]http://folk.ntnu.no/jonvegar/images/math.gif

I really need some help here (no program is allowed :smile:)
 
Last edited by a moderator:
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What work have you done on the problem so far?
 
I'm not sure why you would consider that "hard". You can solve the second equation for x as a quadratic function of y. Putting that into the first equation gives a cubic equation for y.
 
The problem is to find exact values, not estimatet values. Therefore: do not use any programs...
 
Indeed. Do you have any strategies to find a root? There are many you can try. Once you find one, you can divide and just solve a quadratic.
 
Here is what I have done so far:

[PLAIN]http://folk.ntnu.no/jonvegar/images/1.gif
[PLAIN]http://folk.ntnu.no/jonvegar/images/2.gif
[PLAIN]http://folk.ntnu.no/jonvegar/images/3.gif
[PLAIN]http://folk.ntnu.no/jonvegar/images/4.gif
[PLAIN]http://folk.ntnu.no/jonvegar/images/5.gif
[PLAIN]http://folk.ntnu.no/jonvegar/images/6.gif

But these solutions contains "cos". It is possible to rewrite the equations to the formula
[PLAIN]http://folk.ntnu.no/jonvegar/images/8.gif
and then find solutions without any trigonometrical components.

That is my problem...
 
Last edited by a moderator:
Would have been a simpler computation for the program to have changed the x into 1/y rather than the other way around, small numbers to deal with overall. Were you expected to solve this cubic analytically and it's roots actually looked like that?
 
Yes. It does not matter how you start. You will get the same solutions with the same trigonometrical components. Plz help me find solutions without any trigonometrical components.
 
There is a typo in the problem: "79" should be "78".
 
  • #10
Is it just because the answer drops our nicely if that is the case, or do you somehow know it as a fact :S ?
 
  • #11
I just somehow know it is a fact :smile:
Count Iblis said:
There is a typo in the problem: "79" should be "78".
Sorry mac, it is "79"
 
Last edited:

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