Question

若X²+x-1=0,求多项式x³+2x²-2的值.

Answer 1

x³+2x²-2
=x³+x²-x+x²+x-1-1
=x(x²+x-1)+(x²+x-1)-1
=0+0-1
=-1

追问

谢谢！虽然老师已经讲过了，而且答案过程都不一样！！！
x²+x-1=0

x²=1-x

x³+2x²-2

=x²·x+2·x²-2

=x(1-x)+2·(1-x)-2
=x-x²+2-2x
=x-(1-x)+2-2x
=x-1+x+2-2x
=1

追答

x²+x-1=0

x²=1-x

x³+2x²-2
=x²·x+2·x²-2
=x(1-x)+2·(1-x)-2
=x-x²+2-2x-2
=x-(1-x)+2-2x-2
=x-1+x+2-2x-2
=1-2
=-1