SOLUTION: x^4 +y^4 = Where x+y = a and xy = b

Algebra ->  Real-numbers -> SOLUTION: x^4 +y^4 = Where x+y = a and xy = b      Log On


   

Question 964064: x^4 +y^4 =
Where x+y = a and xy = b
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2By%29%5E4=x%5E4%2B4x%5E3y%2B6x%5E2y%5E2%2B4xy%5E3%2By%5E4
4x%5E3y%2B4xy%5E3=4xy%28x%5E2%2By%5E2%29
%28x%2By%29%5E2=x%5E2%2B2xy%2By%5E2
x%5E2%2By%5E2=%28x%2By%29%5E2-2xy
So then,
x%5E4%2By%5E4=%28x%2By%29%5E4-4x%5E3y-6x%5E2y%5E2-4xy%5E3
x%5E4%2By%5E4=%28x%2By%29%5E4-6x%5E2y%5E2-4xy%28x%5E2%2By%5E2%29
x%5E4%2By%5E4=%28x%2By%29%5E4-6%28xy%29%5E2-4xy%28%28x%2By%29%5E2-2xy%29
Substituting,
x%5E4%2By%5E4=%28a%29%5E4-6b%5E2-4b%28%28a%29%5E2-2b%29
x%5E4%2By%5E4=%28a%29%5E4-6b%5E2-4a%5E2b%2B8b%5E2
highlight%28x%5E4%2By%5E4=a%5E4-4a%5E2b%2B2b%5E2%29