若x^2-3x+1=0,则(2x^5-5x^4+2x^3-8x^2)/(x^2+1)的值是多少?

问题描述:

若x^2-3x+1=0,则(2x^5-5x^4+2x^3-8x^2)/(x^2+1)的值是多少?

∵x^2-3x+1=0
∴x^2+1=3X
∴(2x^5-5x^4+2x^3-8x^2)/(x^2+1)
=[2X^3(X^2-3x+1)+x^2(x^2-3x+1)+3x(x^2-3x+1)-3x]/3x
=-3x/3x
=-1