若lg(x-y)+lg(x+2y)=lg2+lgx+lgy,则log√2(x/y)=
问题描述:
若lg(x-y)+lg(x+2y)=lg2+lgx+lgy,则log√2(x/y)=
答
(x-y)(x+2y)=2xy
x²+xy-2y²=2xy
x²-xy-2y²=0
(x-2y)(x+y)=0
x=2y x=-y 舍去
把x=2y代入得
lg√2(x/y)=lg2