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0<x,0<y,x+y=1, 求(x+1/x)(y+1/y)最小值，
解(x+1/x)(y+1/y)=xy+1/xy+y/x+x/y=xy+1/xy+{(x+y)(x+y)-2xy}/xy=2/xy+xy-2是递减函数在0<xy<=1/4.
X=y=1/2时取最小值25/4.