设正数x,y满足log2(x+y+3)=log2x+log2y,求x+y取值范围——[6,+∞)_数学解答

设正数x,y满足log2(x+y+3)=log2x+log2y,求x+y取值范围——[6,+∞)

人气：495 ℃　时间：2020-06-11 02:40:35

解答

log2(x+y+3)=log2x+log2y＝log2xy
所以x+y+3＝xy
又x^2-2xy+y^2>=0所以左右加上4xy得到x^2+2xy+y^2>=4xy
所以xy