1)
a^2-3a-1=0
a-3-1/a=0
a-1/a=3
(a-1/a)^2=9
a^2+1/a^2-2=9
a^2+1/a^2=11
(a^2+1/a^2)=121
a^4+1/a^4+2=121
a^4+1/a^4=119
2)
2xy=(x+y)^2-(x^2+y^2)=1-2=-1
xy=-1/2
x^3+y^3=(x+y)(x^2+y^2-xy)=1*(2-(-1/2))=5/2
x^5+y^5=(x^2+y^2)(x^3+y^3)-x^2y^2(x+y)
=2*5/2-(-1/2)^2*1
=5-1/4
=19/4