difficult system: x^8+y^8+z^8+v^3=252, x+y=5, z+v=7, xy=vz

[Edyss]

Hi i have a system that i just cant solve.
x^8+y^8+z^8+v^3=252
x+y=5
z+v=7
xy=vz
I would be really glad if you could post the whole thing solved, thank you

 

[stapel]

I would be really glad if you could post the whole thing solved

I'm sorry, but the policies you saw in the "Read Before Posting" announcement remain in effect; namely, we don't "do" students' work for them, nor do we give out the answers.

I have a system that i just cant solve.
x^8+y^8+z^8+v^3=252
x+y=5
z+v=7
xy=vz

What have you tried? How far have you gotten?

By the way, are you supposed to find all solutions, or only integral or natural-number solutions? What techniques have they given you for this? (Wolfram Alpha gives only decimal approximations, most of which are complex-valued.)

When you reply, please include the original exercise statement and a clear listing of your efforts so far. Thank you!