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Adri

Ketaksamaan $2n$ variabel

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Diberikan bilangan real positif $a_1, a_2, \cdots, a_n$ dan $b_1, b_2, \cdots, b_n$ yang memenuhi:

i) $a_1 a_2 \cdots a_n = b_1 b_2 \cdots b_n$, dan

ii) $\displaystyle \sum_{1\leq i < j \leq n} \left| a_i -a_j \right|\leq \sum_{1\leq i < j \leq n} \left| b_i -b_j \right|$

Buktikan bahwa

\[\sum_{i=1}^n a_i \leq (n-1) \sum_{i=1}^n b_i\]

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waaah, rusuh sekali (-___-; )

Makanya pak, wkwkwk, ini bisa jadi soal IMO susah sih.. atau A7, A8 gitu...

Bagian keduanya minta buktiin klo $n-1$ diatas tidak bisa diganti dengan yang lebih kecil (ini easier)

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