### simplify roots with mulitple inbedded roots

Hi everyone,

I know this questions has been asked quite some times before and I've browsed a couple of hours searching for the answer but I haven't found anything that worked yet. So here it is:

So I have these two functions and I need to calculate k. I've found you can use the maxima_methods, but as you can see, it doesn't work here either. (I tested the example question and I could simplify that one with these commands, so it's not the virtual machine)

I know you can calculate it by using the maxima engine itself on the virtual machine en then you should find 37/4+3*sqrt(7). But isn't there any method a bit less far-fetched, and I also still need to find a way to switch to maxima on the cloud, so this solution is for the virtual machine only...

I'm working on a project for school concerning Sage and so far this is the only problem I've encountered.

Thanks in advance!