题目

已知x1、x2为方程xˆ2+3x+1=0的两实根,求代数式x1ˆ3+8x2 20的值

提问时间：2020-12-12

答案

x1+x2=-3
x1x2=1
x1²＋3x1+1=0
x1²=-3x1-1
所以
x1ˆ3+8x2+20
=x1 (x1²)+8x2+ 20
=x1·(-3x1-1)+8x2+ 20
=-3x1²-x1+8x2+ 20
=-3(-3x1-1)-x1+8x2+ 20
=9x1+3-x1+8x2+ 20
=8x1+8x2+23
=8(x1+x2)+23
=8×(-3)+23
=-24+23
=-1