lg(x+y)+lg(2x+3y)-lg3=lg4+lgx+lgy求x/y

问题描述:

lg(x+y)+lg(2x+3y)-lg3=lg4+lgx+lgy求x/y

lg(x+y) + lg(2x+3y) - lg3= lg4+lgx+lgylg(x+y)+ lg(2x+3y) = lg3 +lg4+lgx+lgylg[(x+y)*(2x+3y)] = lg[ 3*4*xy)(x+y)(2x+3y)=12xy 2x^2+5xy+3y^2=12xy2x^2-7xy+3y^2=0,(2x-y)(x-3y)=02x=y或x-3y=0x/y=1/2或x/y=3