已知代数式m²+m-1=0,那么代数值m三次方+2m²+2009=

问题描述:

已知代数式m²+m-1=0,那么代数值m三次方+2m²+2009=

2010

m三次方+2m²+2009=m³+m²-m+m²+m-1+2010=m(m²+m-1)+(m²+m-1)+2010=2010

∵m²+m-1=0,所以(m²+m-1)m=0∴(m²+m-1)m=m³+m²-m=0m³+2m²+2009=m³+m²-m+m²+m-1+2010=(m²+m-1)m+(m²+m-1)+2010=2010 ...

m²+m-1=0 ----> m²+m=1
m三次方+2m²+2009=m^3+m²+m²+2009=m( m²+m)+m²+2009=m+m²+2009=1+2009=2010