Solve (ab)^2 + ab - a^2 - 4b^2 = 0

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Homework Help Overview

The problem involves solving the equation (ab)^2 + ab - a^2 - 4b^2 = 0 for the variable 'a', treating 'b' as a constant. This falls within the subject area of algebra, specifically focusing on quadratic equations.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss treating the equation as a quadratic in 'a', with suggestions to rearrange it into the standard form of a quadratic equation. There is mention of potentially using the quadratic formula to find solutions for 'a'. Some participants express uncertainty about the approach, considering the nature of the equation as possibly related to Diophantine equations.

Discussion Status

The discussion is active, with multiple participants suggesting similar approaches to treat the equation as a quadratic. There is no explicit consensus, but the guidance provided indicates a productive direction for solving the equation.

Contextual Notes

Participants are considering the implications of treating 'b' as a constant and exploring the structure of the equation without resolving it. There is an acknowledgment of the need for clarity in the approach to solving the equation.

soopo
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Homework Statement



Solve the following equation for `a`.
(ab)^2 + ab - a^2 - 4b^2 = 0


The Attempt at a Solution



ab( ab + 1 ) - a^2 -4b^2 =

I perhaps should now use some sort of Diophantine equation.
However, I am not sure.
 
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Just treat it as a quadratic equation in 'a', regarding 'b' as a constant.
 
hiya,

treat b like a constant.
maybe the best way to solve this for a is to put the equation in the form of a quadratic, like:
ax^2+bx+c=0
(in this case you will have a instead of x) then use the quadratic formula to find the value(s) for a.
 
Dick said:
Just treat it as a quadratic equation in 'a', regarding 'b' as a constant.

sara_87 said:
hiya,

treat b like a constant.
maybe the best way to solve this for a is to put the equation in the form of a quadratic, like:
ax^2+bx+c=0
(in this case you will have a instead of x) then use the quadratic formula to find the value(s) for a.
Two great minds with a single thought!
 

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