若a,b,c>0,两直线y=xlg(ac)+m和y=xlg(bc)+n互相垂直,求a/b的取值范围

由题意可知lg(ac)=-1/lg(bc)（lga+lgc)(lgb+lgc)=-1(lgc)^2+(lga+lgb)lgc+lgalgb+1=0△=(lga+lgb)^2-4(lgalgb+1)≥0(lga-lgb)^2-4≥0lga-lgb≥2或lga-lgb≤-2a/b≥100或0≤a/b≤1/100