Question

设x>0,y>0,且xy-(x+y)=1,求x+y的取值范围

设x>0,y>0,且xy-(x+y)=1,求x+y的取值范围

Answer 1

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