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

题目

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

答案

由题意 x1^2+3x1+1=0
x1^2=-1-3x1
原式=x1*x1^2+8x2+20
=x1(-1-3x1)+8x2+20
=-3x1^2-x1+8x2+20
=-3(-1-3x1)-x1+8x2+20
=8x1+8x2+23
=8(x1+x2)+23
=8(-3)+23
=-1