已知x²+x-1=0,那么代数式x³+2x²-7的值为

已知x²+x-1=0,那么代数式x³+2x²-7的值为
已知x²+x-1=0,那么代数式x³+2x²-7的值为

已知x²+x-1=0,那么代数式x³+2x²-7的值为
x^2+x-1=0
x^3=-x^2+x
x^3+2x^2-7
=-x^2+x+2x^2-7
=x^2+x-7
=1-7
=-6

x²+x-1=0
x²+x=1

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

x³+2x²-7
=x(x²+x-1)+x²+x-7 注：用0代x²+x-1得：
=x²+x-7
=(x²+x-1)-6
=-6

∵x²+x-1=0
∴x²+x=1，x²=1-x
∴x³+2x²-7=x*x²+2x²-7=x(1-x)+2x²-7=x²+x-7=-6