m是方程x²+x-1=0的根,则式子m³+2m²+2011的值为

m是方程x²+x-1=0的根,则式子m³+2m²+2011的值为
m是方程x²+x-1=0的根,则式子m³+2m²+2011的值为

m是方程x²+x-1=0的根,则式子m³+2m²+2011的值为
x=m代入方程：m²+m-1=0 ①
两边乘以m:m³+m²-m=0 ②
①+②:m³+2m²-1=0
所以:m³+2m²+2011=2012