How Can You Solve the Equation (U2-U1)=259.2(U2*U1) with Two Unknowns?

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Discussion Overview

The discussion revolves around solving the equation (U2-U1)=259.2(U2*U1) with two unknowns, U1 and U2. Participants explore various approaches to find solutions, including iterative methods and algebraic manipulations, while considering the implications of the equation in different contexts.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant notes that there is one equation with two unknowns, suggesting that there is no unique solution.
  • Another participant proposes setting U1=0 and U2=0 as one possible solution, indicating that the set of all solutions forms a hyperbola.
  • Some participants suggest that additional context about U1 and U2 could allow for a solution, such as if they represent sides of a rectangle with area restrictions.
  • A participant transforms the original equation to find the ratio U2/U1, leading to a quadratic equation that can be solved for x=U2/U1.
  • It is mentioned that the constant 259.2 relates to drag and is derived from delta t, with a focus on determining how much speed drops, represented as delta U.
  • Another participant emphasizes that knowing one value (either U2 or U1) allows for calculating the other and determining U2-U1.

Areas of Agreement / Disagreement

Participants generally agree that there is no unique solution due to the presence of two unknowns. However, multiple approaches and interpretations of the equation remain, indicating ongoing debate and exploration of potential solutions.

Contextual Notes

Participants highlight the dependence on the definitions and contexts of U1 and U2, as well as the limitations of the equation in providing a singular solution without additional information.

skaboy607
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Hi

I have the following equation:

(U2-U1)=259.2(U2*U1)

Both U1 and U2 are unknowns. Its been suggested to use an iterative process like Newton Raphson to solve but all examples using this technique are only for one unknown.

(U2-U1) is the value of interest.

Thanks
 
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You have 1 equation with 2 unknowns.
There is no single solution for that.

If you want a solution, you can take U1=0 and U2=0.

The set of all solutions is a hyperbola.
 
skaboy607 said:
(U2-U1) is the value of interest.

Thanks

I don't see a way to solve for the difference between the variables, but you can solve for the ratio of them U2/U1.

U2/U1-U1/U2=259.2

Let x=U2/U1

x-1/x=259.2

x^2-259.2x-1=0

Now you can solve the quadratic.
 
Last edited:
Its an equation for drag that has been reduced to its current format. The constant 259.2 comes from the delta t. I need to find how much the speed drops by, i.e. delta U.
 
skaboy607 said:
I need to find how much the speed drops by, i.e. delta U.

The ratio U2/U1 could be considered a measure of how much the speed drops by. And, once you know one value (either U2 or U1) you can calculate the other and identify U2-U1.
 

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