正实数x,y满足2x+y+6=xy
∵2x+y≥2√2xy
∴2√2xy+6≤xy
∴xy-2√2xy-6≥0
∴√xy≥3√2或√xy≤-√2﹙舍﹚
∴xy≤18
则xy的最小值是18.
若正实数x,y满足2x+y+6=xy,则xy的最小值是?答案是18,
正实数x,y满足2x+y+6=xy
∵2x+y≥2√2xy
∴2√2xy+6≤xy
∴xy-2√2xy-6≥0
∴√xy≥3√2或√xy≤-√2﹙舍﹚
∴xy≤18
则xy的最小值是18.