若m^2+m-1=0,试探求m^4+2m^3+m^2+的值?
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/23 17:30:57
![若m^2+m-1=0,试探求m^4+2m^3+m^2+的值?](/uploads/image/z/5539828-4-8.jpg?t=%E8%8B%A5m%5E2%2Bm-1%3D0%2C%E8%AF%95%E6%8E%A2%E6%B1%82m%5E4%2B2m%5E3%2Bm%5E2%2B%E7%9A%84%E5%80%BC%3F)
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?
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