设正数xy满足log2(x+y+3)=log2x+log2y,求xy取值范围
问题描述:
设正数xy满足log2(x+y+3)=log2x+log2y,求xy取值范围
答
由已知
log2(x+y+3)=log2(xy)
可得xy=x+y+3≥2√xy+3
得(√xy-3)(√xy+1)≥0
得√xy≥3
得xy≥9