Question

已知X1与X2为方程X²+5X+2=0的两实根，则X1²+23X2+5=

Answer 1

x^2+5x+2=0
把x=x1代入
x1^2+5x1+2=0
x1^2=-5x1-2
所以
x1^3+23x2+5
=x1(-5x1-2)+23x2+5
=-5x1^2-2x1+23x2+5
=-5*(-5x1-2)-2x1+23x2+5
=23x1+23x2+15
由韦达定理
x1+x2=-5
原式=23*(-5)+15
=-100

Answer 2

x₁与x₂为方程x²+5x+2=0的两实根
所以(x+5/2)²=21/4
解出方程有2根：(√21-5)/2、(-√21-5)/2
当x₁=(√21-5)/2，x₂=(-√21-5)/2时，
x₁²+23x₂+5
=(√21-5)²/4+23*(-√21-5)/2+5
=-41-14√21
当x₂=(√21-5)/2，x₁=(-√21-5)/2时，
x₁²+23x₂+5
=(-√21-5)²/4+23*(√21-5)/2+5
=14√21-41

刚看了一楼的，那是x₁²不是x₁³啊

Answer 3

-100,64或16.96