已知x^3-7x+1=0 求x^8-6x^6+3x^5-7x^4-12x^3+2x^2-7x+6的值
问题描述：
已知x^3-7x+1=0 求x^8-6x^6+3x^5-7x^4-12x^3+2x^2-7x+6的值
答
答案为5
答
就是构造多项式x³-7x+1
x^8-6x^6+3x^5-7x^4-12x^3+2x^2-7x+6
=x^8-7x^6+x^5+x^6-7x^4+x^3+2x^5-14x^3+2x^2+x^3-7x+1+5
=x^5(x^3-7x+1)+x^3(x^3-7x+1)+2x^2(x^3-7x+1)+(x^3-7x+1)+5
=5