Hi guys, my lecturer recently did this in class and told us to check it ourselves but I'm having trouble.

We have the solution
<br />
A_{a,b} = \frac{\beta + 2\alpha^2 - 2\alpha \pm \sqrt{\beta^2 - 4 \beta (1-\alpha)}}{2(\alpha^2 +\beta)}<br />
making sense only if \beta > 4(1-\alpha).

He then writes Taylor expanding as \beta \to \infty

A_a = 1-\frac{1}{\beta}+O\left(\frac{1}{\beta^2}\right)

A_b = \frac{(\alpha-1)^2}{\beta}

Which I just cannot seem to understand. Any help in understanding would be greatly appreciated,