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證明:由柯西不等式可知2[(a+1/a)²;+(b+1/b)²;]≥[a+1/a)+(b+1/b)]²;=[3+(a/b)+(b/a)]²;≥(3+2)²;=25.====>(a+1/a)²;+(b+1/b)²;≥25/2.等號僅當a=b=1/2時取得.
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