Solve using quadratic formula?

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Homework Help Overview

The discussion revolves around solving a system of equations involving two variables, θ1 and θ2, defined by their sum and product. The original poster attempts to use the quadratic formula to find the solutions but encounters unexpected results, leading to confusion about the number of solutions.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the method of substituting one variable in terms of another and forming a quadratic equation. Questions arise about the derivation of multiple solutions and the symmetry of the equations.

Discussion Status

Some participants provide guidance by noting the symmetry in the equations and suggesting that the original poster may have made an error in their calculations. There is an ongoing exploration of how the equations relate to each other and the implications for the number of solutions.

Contextual Notes

Participants are considering the implications of the equations being symmetric and questioning the assumptions made about the number of solutions derived from the quadratic formula.

Kinetica
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Homework Statement



Hey guys, recently, I struggled to solve this equation.
I need to find θ1 and θ2 by using this system of equations:

θ12
θ12

After letting θ2=β/θ1, I plugged this into the first equation. I got:

θ12-γθ1+β=0

At this point I get a very unsexy θ1 result by using quadratic solution.

Need you help!

P.S. This way, I get 4 solutions overall, but my professor is saying that there should only be 2 solutions.
 
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Kinetica said:

Homework Statement



Hey guys, recently, I struggled to solve this equation.
I need to find θ1 and θ2 by using this system of equations:

θ12
θ12

After letting θ2=β/θ1, I plugged this into the first equation. I got:

θ12-γθ1+β=0

At this point I get a very unsexy θ1 result by using quadratic solution.

Need you help!

What you've done so far is just fine. And I don't think the answer is going to pretty no matter how you do it.
 
Kinetica said:

Homework Statement



Hey guys, recently, I struggled to solve this equation.
I need to find θ1 and θ2 by using this system of equations:

θ12
θ12

After letting θ2=β/θ1, I plugged this into the first equation. I got:

θ12-γθ1+β=0

At this point I get a very unsexy θ1 result by using quadratic solution.

Need you help!

P.S. This way, I get 4 solutions overall, but my professor is saying that there should only be 2 solutions.

How did you get 4 solutions? Could you show us? The point is that you must have made an error, and we cannot help until we know what you did.

RGV
 
If you look at your equations they are symmetric between θ1 and θ2. You could say there is no difference between θ1 and θ2. Or, do what you did to get a quadratic equation for θ1 but do it to get an equation for θ2 instead - you find you have got exactly the same equation for θ2 as you got for θ1.

You haven't really got two quadratic equations, you've got one.
 

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