证明:当a>1时,不等式a^3+1/a^3>a^2+1/a^2成立
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![证明:当a>1时,不等式a^3+1/a^3>a^2+1/a^2成立](/uploads/image/z/6931959-15-9.jpg?t=%E8%AF%81%E6%98%8E%EF%BC%9A%E5%BD%93a%EF%BC%9E1%E6%97%B6%2C%E4%B8%8D%E7%AD%89%E5%BC%8Fa%5E3%EF%BC%8B1%EF%BC%8Fa%5E3%EF%BC%9Ea%5E2%EF%BC%8B1%EF%BC%8Fa%5E2%E6%88%90%E7%AB%8B)
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证明:当a>1时,不等式a^3+1/a^3>a^2+1/a^2成立
证明:当a>1时,不等式a^3+1/a^3>a^2+1/a^2成立
证明:当a>1时,不等式a^3+1/a^3>a^2+1/a^2成立
证:a^3+1/a^3-(a^2+1/a^2) =1/a^3(a^6+1-a^5-a) =1/a^3(a^5-1)(a-1) ∵a>1 ∴1/a^3(a^5-1)(a-1)>0 a^3+1/a^3-(a^2+1/a^2)>0 a^3+1/a^3>a^2+1/a^2>0