已知a>0,b>0,a+b=1,求证：（a+1/a)(b+1/b)≥25/4

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左式=ab+a/b+1/ab+b/a
=(a2b2+a2+1+b2)/ab
=[a2b2+(1-2ab)+1]/ab
=[(ab-1)2+1]/ab
(ab-1)2+1≥25/16,0

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