已知x²-2x-1=0,求2x的三次方-3x²-4x+2的值.

已知x²-2x-1=0,求2x的三次方-3x²-4x+2的值.
已知x²-2x-1=0,求2x的三次方-3x²-4x+2的值.

已知x²-2x-1=0,求2x的三次方-3x²-4x+2的值.
解
x²-2x-1=0
x²-2x=1
2x³-3x²-4x+2
=2x(x²-2x)+x²-4x+2
=2x+x²-4x+2
=x²-2x+2
=1+2
=3

x^2-2x-1=0可知x^2-2x=1
所以
2x^3-3x^2-4x+2
=2x^3-4x^2+x^2-4x+2
=2x(x^2-2x)+x^2-4x+2
=x^2-2x+2=3

2x的三次方-3x²-4x+2
=2x³-4x²-2x+x²-2x-1+3
=2x(x²-2x-1)+(x²-2x-1)+3
∵x²-2x-1=0
∴原式=2x×0+0+3=3