Answer:
bro just did this on a TGA
Step-by-step explanation:
A. no solutions and a contradiction
B. infinate solutions and an identity
C. one solution and niether
You get everything you need from factoring the last expression:
![x^4-y^4=-176\sqrt7](https://tex.z-dn.net/?f=x%5E4-y%5E4%3D-176%5Csqrt7)
The left side is a difference of squares, and we get another difference of squares upon factoring. We end up with
![x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)](https://tex.z-dn.net/?f=x%5E4-y%5E4%3D%28x%5E2-y%5E2%29%28x%5E2%2By%5E2%29%3D%28x-y%29%28x%2By%29%28x%5E2%2By%5E2%29)
Plug in everything you know and solve for
:
![-176\sqrt7=(x-y)\cdot4\cdot22\implies x-y=\boxed{-2\sqrt7}](https://tex.z-dn.net/?f=-176%5Csqrt7%3D%28x-y%29%5Ccdot4%5Ccdot22%5Cimplies%20x-y%3D%5Cboxed%7B-2%5Csqrt7%7D)