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!

Let $a_n=x^n+y^n$.
Then
$$3a_n=(x+y)a_n=x^{n+1}+xy^n+yx^n+y^{n+1}=a_{n+1}+xya_{n-1}=a_{n+1}+3a_{n-1}$$
and so
$a_{n+1}=3a_n-3a_{n-1}$.
Also, $a_0=x^0+y^0=2$, $a_1=x+y=3$.
So $a_2=3a_1-3a_0=3$, $a_3=3a_2-3a_1=0$, and so on.
