Question

已知x1和x2是方程x2+3x+1=0的两个实数根,则x13+8 x2+20=

Answer 1

x1和x2是方程x²＋3x＋1=0的根,则：x1²＋3x1＋1=0即：x1²=－3x1－1；x1＋x2=－3,x1x2=1

则：

x1³＋8x2＋20

=x1(－3x1－1)＋8x2＋20

=－3x1²－x1＋8x2＋20

=－3(－3x1－1)－x1＋8x2＋20

=8x1＋8x2＋23

=8(x1＋x2)＋23

=－24＋23

=－1