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
A_{a,b} = \frac{\beta + 2\alpha^2 - 2\alpha \pm \sqrt{\beta^2 - 4 \beta (1-\alpha)}}{2(\alpha^2 +\beta)}
making sense only if $\displaystyle \beta > 4(1-\alpha).$

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

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

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

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