设x>0,y>0,且xy-(x+y)=1,求x+y的取值范围
问题描述:
设x>0,y>0,且xy-(x+y)=1,求x+y的取值范围
答
xy≤[(x+y)/2]^2 所以xy=1+x+y≤[(x+y)/2]^2即(x+y)^2-4(x+y)-4≥0解得x+y≤-2√2+2(舍)或x+y≥2√2+2 得到范围
x+y≥2√2+2