方程(lg2x)*(lg3x)=-a2(次方)有两个相异实根，求a的范围 和两根实积

(lg2x)*(lg3x)=-a^2,
(lg2+lgx)*(lg3+lgx)=-a^2,
(lgx)^2+(lg2+lg3)*lgx+lg2*lg3+a^2=0.....,,(1)
判别式(lg2+lg3)^2-4*(lg2*lg3+a^2)>0,
(lg2)^2+2*lg2*lg3+(lg3)^2-4*lg2*lg3>4a^2,
(lg3-lg2)^2>4a^2,
a的范围是-(lg3/2)/2<a<(lg3/2)/2.
设两根是x1,x2,由(1),lgx1+lgx2=-lg2-lg3,
lg(x1*x2)=lg(1/6),
x1*x2=1/6.