已知x,y是方程z²+3z+1=0的两个实数根,则x²+8y+20=?

已知x,y是方程z²+3z+1=0的两个实数根,则x²+8y+20=?
已知x,y是方程z²+3z+1=0的两个实数根,则x²+8y+20=?

已知x,y是方程z²+3z+1=0的两个实数根,则x²+8y+20=?
已知x,y是方程z²+3z+1=0的两个实数根,
z1=(-3+√3^2-4)/2=(-3+√5)/2
或z2=(-3-√3^2-4)/2=(-3-√5)/2
(1)当x=(-3+√5)/2 y=(-3-√5)/2
则x²+8y+20
=((-3+√5)/2)^2+8*(-3-√5)/2+20
=(9-6√5+5)/4+4*(-3-√5)+20
=7/2-3√5/2-12-4√5+20
=23/2-11√5/2
(2)当x=(-3-√5)/2 y=(-3+√5)/2
则x²+8y+20
=((-3-√5)/2)^2+8*(-3+√5)/2+20
=(9+6√5+5)/4+4*(-3+√5)+20
=7/2+3√5/2-12+4√5+20
=23/2+11√5/2