Question

m^2+m-1=0 求2m^3+4m^2+2006的值

如题.
m^2+m-1=0 求2m^3+4m^2+2006的值

Answer 1

m^2+m-1=0 得到m^2+m=1

2m^3+4m^2+2006=2m(m^2+m)+2m^2+2006=2m+2m^2+2006=2(m^2+m)+2006=2008

Answer 2

由m^2+m-1=0得m^2+m=1
2m^3+4m^2+2006=2m(m^2+m)+2m^2+2006=2m(m^2+m)+2(1-m)+2006
将m^2+m=1代入，得
原式=2m+2-2m+2006=2008