柯西、均值不等式的简单问题- -已知a+b+c=1且abc都为正数.求(a+1/a)2+(b+1/b)2+(c+1/c)2的最小值已知a+b+c=1且abc都为正数.求(a+1/a)2+(b+1/b)2+(c+1/c)2的最小值原式=a2+2+1/a2+b2+2+1/b2+c2+2+1/c2=(a2+b2+c2)+(1/a2+1/b2
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![柯西、均值不等式的简单问题- -已知a+b+c=1且abc都为正数.求(a+1/a)2+(b+1/b)2+(c+1/c)2的最小值已知a+b+c=1且abc都为正数.求(a+1/a)2+(b+1/b)2+(c+1/c)2的最小值原式=a2+2+1/a2+b2+2+1/b2+c2+2+1/c2=(a2+b2+c2)+(1/a2+1/b2](/uploads/image/z/2449940-68-0.jpg?t=%E6%9F%AF%E8%A5%BF%E3%80%81%E5%9D%87%E5%80%BC%E4%B8%8D%E7%AD%89%E5%BC%8F%E7%9A%84%E7%AE%80%E5%8D%95%E9%97%AE%E9%A2%98-+-%E5%B7%B2%E7%9F%A5a%2Bb%2Bc%3D1%E4%B8%94abc%E9%83%BD%E4%B8%BA%E6%AD%A3%E6%95%B0.%E6%B1%82%EF%BC%88a%2B1%2Fa%292%2B%28b%2B1%2Fb%292%2B%28c%2B1%2Fc%292%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E5%B7%B2%E7%9F%A5a%2Bb%2Bc%3D1%E4%B8%94abc%E9%83%BD%E4%B8%BA%E6%AD%A3%E6%95%B0.%E6%B1%82%EF%BC%88a%2B1%2Fa%292%2B%28b%2B1%2Fb%292%2B%28c%2B1%2Fc%292%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E5%8E%9F%E5%BC%8F%3Da2%2B2%2B1%2Fa2%2Bb2%2B2%2B1%2Fb2%2Bc2%2B2%2B1%2Fc2%3D%28a2%2Bb2%2Bc2%29%2B%281%2Fa2%2B1%2Fb2)
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