设√2≤x1＜x2,则f(x1)-f(x2)=x1+2/x1-x2-2/x2=(x1-x2)+2(x2-x1)/x1x2=(x1-x2)(1-2/x1x2)因为√2≤x1＜x2,所以x1-x2＜0,x1x2＞2,1-2/x1x2＞0,所以f(x1)-f(x2)＜0,即f(x1)＜f(x2).因此,f(x)=x+2/x在[根号2,正无穷）上...