Solving Quadratic Equations with Parameters | Step-by-Step Guide

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Homework Help Overview

The discussion revolves around solving quadratic equations involving parameters, specifically with equations defined as x=t^2 + t and y=t^2 - t. Participants are exploring methods to manipulate these equations to express one variable in terms of the other.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss setting the quadratic equations equal to one another and express confusion about the next steps. There are suggestions to subtract the equations to find a relationship between x and y, and questions about the implications of eliminating the parameter t.

Discussion Status

Some participants have offered hints and alternative approaches, such as expressing t in terms of x and y. However, there is no explicit consensus on the best method to proceed, and multiple interpretations of the problem are being explored.

Contextual Notes

Participants are grappling with the complexity of the resulting expressions and the challenge of eliminating the parameter while maintaining clarity in the equations.

razored
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Homework Statement


x=t^2 +t
y=t^2-t


Homework Equations


quadratic equation


The Attempt at a Solution


0=t^2-t-x
0=t^2+t+y
[tex] 0=\frac{-1 +- \sqrt{1+4x}}{2}<br /> 0=\frac{1 +- \sqrt{1+4y}}{2}[/tex]

Aftert i set the to quadratics equal to one another, I do not know what to do. Any help?
 
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The results of the quadratic equations are t, not zero. But you are still doing it the hard way. Subtract the two original equations to get an expression for t in terms of x and y. Then substitute the resulting t back into one of the equations.
 
razored said:
x=t^2 +t
y=t^2-t

Hi razored! :smile:

Hint: go for the obvious … what is x + y? :wink:
 
Subtracting y from x leaves me with [tex]0=x^2 -2xy+y^2-2y-2x[/tex] which is ugly. Is there anything I can do to find to y= ? No, right?

Thank you.
 
What's to do about it? You eliminated the parameter. Isn't that what they asked for? Trying to solve for y will just make it super-ugly.
 

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