设x,y属于(0,正无穷)且xy-(x+y)=1求xy和x+y的取值范围

题目

设x,y属于(0,正无穷)且xy-(x+y)=1求xy和x+y的取值范围

答案

xy=1+(x+y)0 t>2+2根号2
t^2-4t-4>=0 t>=2+2根号2
x+y>=2+2根号2
x+y>=2根号xy xy-1>=2根号xy xy=m
m-1>=2根号m
m^2+1-6m>=0 m>=3+2根号2
xy>=3+2根号2