Question

已知x1、x2是方程x²+3x+1=0的两实数根,则x1³+8x2+20等于多少

Answer 1

x1、x2是方程是根,则：(x1)²＋3(x1)＋1=0,即：(x1)²=－3(x1)－1且x1＋x2=－3

x1³＋8x2＋20

=x1(－3x1－1)＋8x2＋20

=－3(x1)²－x1＋8x2＋20

=3[3x1＋1]－x1＋8x2＋20

=8x1＋8x2＋23

=8(x1＋x2)＋23

=－24＋23

=－1

答的因该是这样,请纳用.