设m^2+m-1=0,求m^3+2m^2+2000的值哈哈!再帮偶算一个!100^2-99^2+98^2-97^2+……+2^2-1
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![设m^2+m-1=0,求m^3+2m^2+2000的值哈哈!再帮偶算一个!100^2-99^2+98^2-97^2+……+2^2-1](/uploads/image/z/4034527-7-7.jpg?t=%E8%AE%BEm%5E2%2Bm-1%3D0%2C%E6%B1%82m%5E3%2B2m%5E2%2B2000%E7%9A%84%E5%80%BC%E5%93%88%E5%93%88%EF%BC%81%E5%86%8D%E5%B8%AE%E5%81%B6%E7%AE%97%E4%B8%80%E4%B8%AA%EF%BC%81100%5E2-99%5E2%2B98%5E2-97%5E2%2B%E2%80%A6%E2%80%A6%2B2%5E2-1)
设m^2+m-1=0,求m^3+2m^2+2000的值哈哈!再帮偶算一个!100^2-99^2+98^2-97^2+……+2^2-1
设m^2+m-1=0,求m^3+2m^2+2000的值
哈哈!再帮偶算一个!
100^2-99^2+98^2-97^2+……+2^2-1
设m^2+m-1=0,求m^3+2m^2+2000的值哈哈!再帮偶算一个!100^2-99^2+98^2-97^2+……+2^2-1
m^2+m-1=0…………①
所以,
m^3+2m^2+2000
=(m^3+m^2-m)+(m^2+m-1)+2001
=m(m^2+m-1)+(m^2+m-1)+2001…………②
把①式代入②式得:
m^3+2m^2+2000=2001
(2) 100^2-99^2+98^2-97^2+…+2^2-1
=(100^2-99^2)+(98^2-97^2)+…+(2^2-1)
=199+195+191+…+3
=(199+3)×25
=5050
m^3+2m^2+2000
=m3+m2-m+m2+m-1+1+200
=m(m2+m-1)+(m2+m-1)+1+2000
=2001
m^2+m-1=0,
m^2+m=1
m^3+2m^2+2000
=m^3+m^2+m^2+m-m+2000
=m(m^2+m)+m^2+m-m+2000
=m*1+1-m+2000
=2001