a²-2ab-9b²=0兩邊同時(shí)除以b²(b²≠0)得
(a/b)²-2(a/b)-9=0
a/b=1±√10
因?yàn)閍,b同號.所以a/b＞0
所以a/b=1+√10
lg(a²+ab-6b²)-lg(a²+4ab+15b²)
=lg[(a²+ab-6b²)/(a²+4ab+15b²)](上下同時(shí)除以b²)
=lg{[(a/b)²+(a/b)-6]/[(a/b)²+4(a/b)+15)]}
=lg{[(1+√10)²+(1+√10)-6]/[(1+√10)²+4(1+√10)+15)]}
=lg[(2+√10)/(10+2√10)]
=lg(√10/10)
=lg10(-1/2)
=-1/2