若lg(a-b)+lg(a+b)=lg2+lga+lgb,求a/b的值
问题描述:
若lg(a-b)+lg(a+b)=lg2+lga+lgb,求a/b的值
答
lg(a-b)+lg(a+b)
=lg(a-b)(a+b)
=lg(aa-bb)
lg2+lga+lgb
=lg2+lgab
=lg2ab
就是aa-bb=2ab
aa-2ab+bb-2bb=0
(a-b)² =2b²
(a/b-1)² =2
(a/b-1) =√2
a/b=1+√2