已知,A和B为方程 X^2+3X+1 = 0 的两个实根,
可得:A^2+3A+1 = 0 ,则有:A^2 = -(3A+1) ;
所以,A^3 = -A(3A+1) = -3A^2-A = 3(3A+1)-A = 8A+3 ;
由韦达定理可得:A+B = -3 ;
所以,A^3+8B+20 = 8A+3+8B+20 = 8(A+B)+23 = -1 .
已知,A和B为方程 X^2+3X+1 = 0 的两个实根,
可得:A^2+3A+1 = 0 ,则有:A^2 = -(3A+1) ;
所以,A^3 = -A(3A+1) = -3A^2-A = 3(3A+1)-A = 8A+3 ;
由韦达定理可得:A+B = -3 ;
所以,A^3+8B+20 = 8A+3+8B+20 = 8(A+B)+23 = -1 .