已知xy大于0求证xy+1/xy+y/x+x/y大于等于4
问题描述：
已知xy大于0求证xy+1/xy+y/x+x/y大于等于4
答
xy+1/xy+y/x+x/y
=[(xy)^2+1+x^2+y^2]/(xy)
=[(xy)^2-2xy+1+x^2-2xy+y^2+4xy]/(xy)
=[(xy-1)^2+(x-y)^2+4xy]/(xy)
=[(xy-1)^2+(x-y)^2]/(xy)+4
∵xy>0
∴[(xy-1)^2+(x-y)^2]/(xy)≥0
因此,xy+1/xy+y/x+x/y≥4