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證: (a+b)(1/a+1/b) =1+a/b+b/a+1 =2+a/b+b/a a>0,b>0 由均值不等式,得:a/b+b/a≥2(當a/b=b/a時,即a=b時,取等號) 2+a/b+b/a≥2+2=4 (a+b)(1/a+1/b)≥4
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