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

[soopo]

1. The problem statement, all variables and given/known data

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


3. 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.

[Dick]

Just treat it as a quadratic equation in 'a', regarding 'b' as a constant.

[sara_87]

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.

[HallsofIvy]

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.
Two great minds with a single thought!