若实数x,y满足lgx+lgy=lg(x+y),则x+y的取值范围是

对数有意义,x>0 y>0lgx+lgy=lg(x+y)lg(xy)=lg(x+y)xy=x+y由均值不等式得(x+y)²≥4xy(x+y)²≥4(x+y)(x+y)²-4(x+y)≥0(x+y)(x+y-4)≥0x+y≥4或x+y≤0(舍去)x+y的取值范围为[4,+∞)...