若m²+m-1=0,求m³+2×m²+2009等于什么
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/08/17 22:16:27
若m²+m-1=0,求m³+2×m²+2009等于什么
![若m²+m-1=0,求m³+2×m²+2009等于什么](/uploads/image/z/8104757-5-7.jpg?t=%E8%8B%A5m%26%23178%3B%2Bm-1%3D0%2C%E6%B1%82m%26%23179%3B%2B2%C3%97m%26%23178%3B%2B2009%E7%AD%89%E4%BA%8E%E4%BB%80%E4%B9%88)
因为 m²+m-1=0--------
所以,m²=1-m,m=1-m²---
m³+2×m²+2009=m²*m+2×m²+2009
=m²*(m+2)+2009
=(1-m)*(m+2)+2009
=m+2-m²-2m+2009
=[(1-m²)-m]+2010 -----------上面有这个m=1-m²---
=2010
----------------------------------------------------------------OK啦---------------------------------
所以,m²=1-m,m=1-m²---
m³+2×m²+2009=m²*m+2×m²+2009
=m²*(m+2)+2009
=(1-m)*(m+2)+2009
=m+2-m²-2m+2009
=[(1-m²)-m]+2010 -----------上面有这个m=1-m²---
=2010
----------------------------------------------------------------OK啦---------------------------------