已知x+1/x=3,求x^4+3x^3-16x^2+3x-17的值

已知x+1/x=3,求x^4+3x^3-16x^2+3x-17的值
已知x+1/x=3,求x^4+3x^3-16x^2+3x-17的值

已知x+1/x=3,求x^4+3x^3-16x^2+3x-17的值
由条件式
x+(1/x)=3
两边乘以x得
x^2-3x+1=0
故x^4+3x^3-16x^2+3x-17
=x^4-3x^3+x^2+6x^3-17x^2+3x-17
=x^2*0+6x^3-18x^2+6x+x^2-3x-17
=6x(x^2-3x+1)+x^2-3x+1-18
=-18

x+1/x=3
x^2+1=3x
x^2-3x+1=0
x^4+3x^3-16x^2+3x-17
=x^2(x^2-3x+1)+6x^3-17x^2+3x-17
=x^2(x^2-3x+1)+6x(x^2-3x+1)+x^2-3x+1-1-17
=(x^2+6x+1)(x^2-3x+1)-18
=0-18
=-18