Question

1、已知m是方程x2-x-4=0的一个根,则代数式m3+m2-6m-7的值为多少

Answer 1

因为m是方程x^2-x-4=0的根,所以

m^2-m-4=0

m^2 = m + 4

m^3 = m^2 + 4m = 5m + 4

m^3 + m^2 = 6m+8

m^3 + m^2 -6m -7 = 6m+8 - 6m -7 =1