已知x²-3x-1=0,求代数2x³-3x²-11x+8得值!

已知x²-3x-1=0,求代数2x³-3x²-11x+8得值!
已知x²-3x-1=0,求代数2x³-3x²-11x+8得值!

已知x²-3x-1=0,求代数2x³-3x²-11x+8得值!
x²-3x-1=0
则：x²=3x+1
原式=2x²*x-3x²-11x+8
=2(3x+1)x-3x²-11x+8 把x²=3x+1代入
=6x²+2x-3x²-11x+8
=3x²-9x+8 再次把x²=3x+1代入
=3(3x+1)-9x+8
=9x+3-9x+8
=11
ps：方法就是不断地降次~

2x³-3x²-11x+8
=2x³-6x²-2x+3x²-9x-3+11
=2x(x²-3x-1)+3(x²-3x-1)+11
=11

x²-3x-1=0
x²=3x+1
2x³-3x²-11x+8
=2x*x²-3x²-11x+8
=2x(3x+1)-3(3x+1)-11x+8
=6x²+2x-9x-3-11x+8
=6(3x+1) -18x+5
=18x+6-18x+5
=11