若m^2+m-1=0,试探求m^4+2m^3+m^2+的值?

若m^2+m-1=0,试探求m^4+2m^3+m^2+的值?

已知：m^2+m-1=0,则：m^2=1-m
m^4+2m^3+m^2
=m^2(m^2+2m+1)
=m^2(1-m+2m+1)
=m^2(m+2)
=m(m^2+2m)
=m(1-m+2m)
=m(m+1)
=m^2+m
=1-m+m
=1

m^2+m-1=0,
即m^2+m=1
那么(m^2+m)^2=1
展开记得问题答案，
m^4+2m^3+m^2=1