已知m²+m=1,求m³-2m+3的值

已知m²+m=1,求m³-2m+3的值
已知m²+m=1,求m³-2m+3的值

已知m²+m=1,求m³-2m+3的值
m^3-2m+3
=m^3-1-2m+4
=(m-1)(m^2+m+1)-2m+4
=2(m-1)-2m+4
=-2+4
=2

m^2=1-m,
m^3=m*m^2=m-m^2
所以m^3-2m+3=m-m^2-2m+3
=-m^2-m+3
=-1+3=2

解m³-2m+3=m(m^2-2+3)=m(m^2+1）
由题意得m=1-m^2
m(m^2+1）=(1-m^2)(1+m^2)=2

m^3-2m+3=m^3+m^2-m^2-2m+3=m(m^2+m)-m^2-2m+3=m*1-m^2-2m+3=-(m^2+m)+3=-1+3=2