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证明 $\forall z_1,z_2,z_3\in\{z\inC:|z|<1\}$,
\begin{multline}\text{cosh}^{-1}\left(1+ \dfrac{2|z_1 - z_2|^2}{(1-|z_1|^2)(1-|z_2|^2)}\right)+\text{cosh}^{-1}\left(1+ \dfrac{2|z_2 - z_3|^2}{(1-|z_2|^2)(1-|z_3|^2)}\right)\\\ge\text{cosh}^{-1}\left(1+ \dfrac{2|z_1 - z_3|^2}{(1-|z_1|^2)(1-|z_3|^2)}\right)\end{multline} |
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