Question

solve thisssssss

Answer 1

I only can do a partial proof, wich is when x+y+z = 0 because we can verify, by expanding, that:
\[(x+y+z)(x^2+y^2+z^2-xy-yz-xz)=x^3+y^3+z^3-3xyz\]
Then if x+y+z = 0,
x^3+y^3+z^3 -3xyz = 0

And 0 is a perfect square.
I think the complete proof can be done by using that identity, but there must be a short way to that , rather than just expand, because if you expand you'll get a 6 grade polinomial with 10 terms wich is almost impossible to factorize.

Answer 2

yes i know

Answer 3

i think you might just have to plug in the first equation in the thing you're supposed to prove and then factor the f (a,b,c) into a hopefully easy to spot perfect square.

seems like the simplest way. i can do maybe do it too if you want

Answer 4

the method really depends which math class/subject/level this is for