Evaluate $x+y=xy=3$ how would you evaluate $x^4+y^4$? I know how to evaluate $x^3 +y^3$ when $x+y=xy=3$, but how would you evaluate for? 

$$x^4+y^4$$

Any help would be appreciated.Thanks in advance!

We have $$81=3^4=(x+y)^4\\=x^4+4x^3y+6x^2y^2+4xy^3+y^4\\=x^4+12x^2+54+12y^2+y^4\\=x^4+y^4+12(x^2+y^2)$$so once you solve for $x^2+y^2$, it should be straight-forward to solve for $x^4+y^4$.
