设x>0,y>0 且xy-(x+y)=1,则x+y的最小值是(请详解)
问题描述:
设x>0,y>0 且xy-(x+y)=1,则x+y的最小值是(请详解)
答
xy-1=x+y≥2√xy xy-2√xy-1≥0 √xy≥1+√2,或√xy≤1-√2(舍去) x+y最小值=2√xy=2+2√2
设x>0,y>0 且xy-(x+y)=1,则x+y的最小值是(请详解)
xy-1=x+y≥2√xy xy-2√xy-1≥0 √xy≥1+√2,或√xy≤1-√2(舍去) x+y最小值=2√xy=2+2√2