已知X1,X2为方程X的平方+3X+1=0的两个实数根，则X1的3次方+8X2+20=? 求过程

Question

如题所述

Answer 1

X1,X2为方程x�0�5+3x+1=0的两根
那么 x1�0�5+3x1+1=0
x1�0�5=-3x1-1
x1（-3x1-1）+8x2+20
=-3x1�0�5-x1+8x2+20
=-3（-3x1-1）-x1+8x2+20
=8（x1+x2）+23
=8×（-3） +23
=-1

Answer 2

x^2+3x+1=0x1+x2=-3，x1x2=1，x1^2=-3x1-1x1^3+8x2+20=x1*(-3x1-1)+8x2+20=-3x1^2-x1+8x2+20=-3(-3x1-1)-x1+8x2+20=9x1+3-x1+8x2+20=8(x1+x2)+23=-24+23=-1

Answer 3

X1^2+3X1+1=0（方程的解满足方程）X1^3=X1*X1^2=X1*(-1-3X1)=-X1-3X1^2=-X1-3（-1-3X）=8X1+3X1的3次方+8X2+20=8X1+3+8X2+20=8(X1+X2)+23=-24+23=-1