已知m²+m-4=0,求m四次方+2m三次方-m-2009

已知m²+m-4=0,求m四次方+2m三次方-m-2009
已知m²+m-4=0,求m四次方+2m三次方-m-2009

已知m²+m-4=0,求m四次方+2m三次方-m-2009
已知等价于：m² = 4-m,利用该式降次,
所以 m^4 = (4-m)² = m² -8m +16 = (4-m)-8m+16=20-9m,
m^3 = m*(4-m)=4m-m²=5m-4,
原式=20-9m + 2(5m-4) - m -2009 = -1997.