x²+x-1=0,那么代数式x³+2x²-7的值为 A.6 B.8 C.-6 D.-8

x²+x-1=0,那么代数式x³+2x²-7的值为 A.6 B.8 C.-6 D.-8
x²+x-1=0,那么代数式x³+2x²-7的值为 A.6 B.8 C.-6 D.-8

x²+x-1=0,那么代数式x³+2x²-7的值为 A.6 B.8 C.-6 D.-8
x²+x-1=0
x³+2x²-7=x(x²+x)+x²-7=x²+x-7=1-7=-6

c

C.-6

c

x³+2x²-7
=x³+x²-x+x²+x-1-6
=x(x²+x-1)+(x²+x-1)-6
=-6

x³+2x²-7=x³+x²-x+x²+x-7=x(x²+x-1)+(x²+x-1)-6=-6

由题可知：x²+x-1=0，所以x²=1-x,x²+x=1
x³+2x²-7=x²(x+2)-7=(1-x)(x+2)-7=x+2-x²-2x-7=-x²-x-5=-(x²+x)-5=-1-5=-6
所以选C