x+1/x=3
x^2+1=3x
x^2=3x-1
x^4+3x^3-16x^2+3x-17
=x^2(3x-1)+3x^3-16x^2+3x-17
=6x^3-17x^2+3x-17
=6x(3x-1)-17x^2+3x-17
=x^2-3x-17
=3x-1-3x-17
=-18