Generalizing inequality problems

One of the things that every students or even teachers aim after solving a problem is whether or not they can generalize that problem. One of the preliminary inequalities for a+b greater or equal than 0 is:

Does it true when the exponent of the inequality is 3?

This leads us to a much bigger question: for k is a positive number, does the inequality still holds for every k? 

As we have generalized the inequality, there are also some exercises that I want to share with you. You can either send me through email or the message below: