急急急。已知m^2+m-2=0,求m^4-4*m^3+m^2+18m-3=? 已知m^2+m-2=0,求m^4-4*m^3+m^2+18m-3=?

m^2+m-2=0
所以m^2+m=2
m^4-4m^3+m^2+18m-3
=m^4+m^3-5m^3+m^2+18m-3
=m^2(m^2+m)-5m^3+m^2+18m-3
=m^2*2-5m^3+m^2+18m-3
=-5m^3+3m^2+18m-3
=-5m^3-5m^2+8m^2+18m-3
=-5m(m^2+m)+8m^2+18m-3
=-5m*2+8m^2+18m-3
=8m^2+8m-3
=8(m^2+m)-3
=8*2-3
=13

先问下你现在在读什么年级

教学程度不同解法也不一样

你初2的吧?
因为m^2+m-2=0
所以m^2=2-m
所以m^4=(2-m)^2=m^2-4m+4=2-m-4m+4=-5m+6,
m^3=(2-m)*m=2m-m^2=2m-(2-m)=3m-2
所以原式=(-5m+6)-4(3m-2)+(2-m)+18m-3=13