设m的平方+m-1=0,则m的立方+2m的平方+2009的值是多少

网友回答

m² + m - 1 = 0
m² + m = 1
m³ + 2m² + 2009
= m³ + m² + m² + 2009
= (m³ + m²) + m² + 2009
= m(m² + m) + m² + 2009
= m + m² + 2009
= 1 + 2009
= 2010======以下答案可供参考======
供参考答案1:
M^2+M-1=0
M^2+M=1
M^2=1-M
M^3=M-M^2
则m^3+2m^2+2009=M-M^2+2M^2+2009=M^2+M+2009=1+2009=2010
供参考答案2:
m的平方+m-1=0,即m^2+m=1
则m^3+2m^2+2009=m^3+m^2+m^2+2009
=m(m^2+m)+m^2+2009
=m+m^2+2009
=1+2009
=2010