x^2-3x+1=0x+(1/x)-3=0x+(1/x)=3x^2+(1/x)^2=(1+1/x)^2-2=9-2=7x^2-(1/x)^2=(x+1/x)^2-4=9-4=5x^3-4x^2+4x+5=x^3-4x^2-3x+1+7x+4=x^3-4x^2-x^2+7x+4=x^3-5x^2+7x+4=x^3-3x^2-2x^2+7x+4=x(x^2-3x)-2x^2+7x+4=-2x^2+6x+4=-2(x^2-3x)+4=2+4=6