m²+m-1=0,求m三次方+2m+2012=

题目

m²+m-1=0,求m三次方+2m+2012=

答案

m^2=1-m,(用降次法,如果求m^3-2m+2012=2011)
m=(-1±√5)/2
m^3+2m+2012
=m(1-m)+2m+2012
=m-(1-m)+2m+2012
=4m+2011
=2(-1±√5)+2011
=2009±2√5.