已知x^2-3x+1=0,求2x^3-3x^2-7x+2009

问题描述:

已知x^2-3x+1=0,求2x^3-3x^2-7x+2009

2x^3-3x^2-7x+2009
=2x^3-6x^2+3x^2-7x+2009
=2(x^3-3x^2+x)-2x+3x^2-7x+2009
=2x(x^2-3x+1)+3x^2-9x+2009
=2x(x^2-3x+1)+3(x^2-3x+1)-3+2009
=0+0+2006=2006