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

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

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

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