已知3x^3-x-1=0,求9x^4+12x^3-3x^2-7x+2001

问题描述:

已知3x^3-x-1=0,求9x^4+12x^3-3x^2-7x+2001

3x^3-x=1
所以原式=9x^4-3x²+12x³-4x-3x+2001
=3x(3x^3-x)+4(3x^3-x)-3x+2001
=3x+4-3x+2001
=2005

3x³-x=1
所以原式=9x^4-3x²+12x³-4x-3x+2001
=3x(3x³-x)+4(3x³-x)-3x+2001
=3x+4-3x+2001
=2005