Question

xy是实数且(x^2+2x+3)(y^2+3/2y+3/1)=9/4则xy等比中项

Answer 1

(x^2+2x+3)[y^2+(2/3)y+1/3]=4/9,

∴y^2+(2/3)y+1/3-4/[9(x^2+2x+3)]=0,x,y是实数,

∴△/4=1/9-{1/3-4/[9(x^2+2x+3)]}

=4/[9(x^2+2x+3)]-2/9

=(-2/9)(x+1)^2/(x^2+2x+3)>=0,

∴x=-1,y=-1/3,

∴x,y的等比中项是土√3/3.