Complicated Limit from Analysis

[nickmai123]

I need some help showing the following limit. I don't really know where to start, and I was just looking for a quick tip or two to begin the proof. Thanks!

Problem:

$$\lim_{n\rightarrow\infty} \sqrt[n]{\alpha^n+\beta^n} = max (\alpha,\beta)$$

 

[8daysAweek]

1. From symmetry, you can assume that alpha >= beta.
2. Now you need to prove that the limit is alpha.
3. Remember the trick where you multiply and then divide by same factor (Think, what factor should it be?).