设m²+m-1=0,求m³+2m²+2013的值

来源：学生作业帮助网 编辑：作业帮 时间：2024/08/09 19:53:07
设m²+m-1=0,求m³+2m²+2013的值
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设m²+m-1=0,求m³+2m²+2013的值
设m²+m-1=0,求m³+2m²+2013的值

设m²+m-1=0,求m³+2m²+2013的值
m³+2m²+2013
=m*m²+2m²+2013
=m(1-m)+2m²+2013
=m+m²+2013
=1+2013
=2014

m²+m-1=0
m²+m=1
m³+2m²+2013
=m(m^2+m)+m^2+2013
=m+m^2+2013
=1+2013
=2014

  1. m=[(根号5)-1]/2

  2. m³+2m²+2013=(4+2根号5)+(3-根号5)+2013

  3. =2020+根号5

  4. 望采纳~

因为
m²+m-1=0
所以
m3+m2-m=0
由上两式想家可得
m³+2m²=1
从而得
m³+2m²+2013=2014

m³+2m²+2013=m(m^2+2m)+2013=m(m+1)+2013=m²+m+2013=1+2013=2014

因为m²+m-1=0 所以m²+m=1
m³+2m²+2013
=m(m²+m)+m²+2013
=m+m²+2013
=2014
OK?