Question

已知X1、X2是方程x^2+3x+1=0的两个实数根,则x1^3+8x2+20=______

Answer 1

X1、X2是方程x^2+3x+1=0的两个实数根

则x1²+3x1+1=0,X1+x2=-3

则x1²+3x1=-1,x1+x2=-3

x1^3+8x2+20

=x1³+3x1²-3x1²+8x2+20

=x1(x1²+3x1)-3x1²+8x2+20

=-x1-3x1²+8x2+20

=-3(x1²+3x1)+8x1+8x2+20

=-3*(-1)+8(x1+x2)+20

=3+8*(-3)+20

=23-24

=-1