令√2<x1<x2
f(x2)-f(x1) = 【x2+2/x2】-【x1-2/x1】
= (x2-x1) + 2/x2-2/x1
= (x2-x1) -2(1/x1-1/x2)
= (x2-x1) -2(x2-x1)/(x1x2)
= (x2-x1){1-2/(x1x2)}
= (x2-x1)(x1x2-2)/(x1x2)
∵√2<x1<x2,∴x2-x1>0,x1x2-2>0,x1x2>0
∴f(x2)-f(x1) >0,f(x2)>f(x1)
∴y=x+(2/x)在(根号2,+无穷)上是增函数