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浅析x > 0,1 < a,(a + x)a与a(a + x)的大小关系
A Study of x > 0, with 1 < a, the Magnitude of (a + x)a versus a(a + x)

DOI: 10.12677/PM.2024.141017, PP. 162-167

Keywords: ba < ab,幂指方程
ba < ab
, Power Index Function

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Abstract:

通过构造重要函数,针对Nam,Kyumin在2023年提出的问题,给出新的直接证明。进一步,我们对问题进行了延展,得到了定性结果。
By constructing important functions, for Nam, Kyumin’s problem in 2023, we give new direct proof. Further, we extend the problem and obtain qualitative results.

References

[1]  Nam, K. (2023) Yet Another Visual Proof That e < a < b?ba< ab. OSF Preprints.
[2]  Nakhli, F. (1987) Proof without Words:πe < eπ. Mathematics Magazine, 60, 165.
https://doi.org/10.1080/0025570X.1987.11977293
[3]  Bikash, C. (2019) A Visual Proof That πe < eπ. The Mathematical Intelligencer, 41, 56.
https://doi.org/10.1007/s00283-018-9816-4
[4]  Haque, N. (2020) A Visual Proof That e < A?eA< Ae. The Mathematical Intelligencer, 42, 74.
https://doi.org/10.1007/s00283-019-09964-x
[5]  Nam, K. (2022) A Visual Proof That e < b?be < eb. OSF Preprints.

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