∵lg(x-2y)=0.5(lgx+lgy)
∴x-2y>0,且x>0,y>0.(1)
由lg(x-2y)=0.5(lgx+lgy) ==>lg(x-2y)=0.5lg(xy)
==>x-2y=√(xy)
==>(x-2y)²=xy
==>x²-4xy+4y²=xy
==>x²-5xy+4y²=0
==>(x-y)(x-4y)=0
解方程得 x=y,或x=4y
∵当x=y时,不满足(1)的条件
当x=4y时,满足条件
∴lg(x-2y)=0.5(lgx+lgy)的解是x=4y.