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lhakonsopoku

Teman Tanya Ineq 3 var

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Buktikan untuk sebarang bilangan real positif $a$, $b$, dan $c$ berlaku
$$
\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge \frac{3}{2}+\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}
$$

Edited by Prihandoko

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Kalikan kedua ruas dengan $(a+b)(b+c)(c+a)$, sederhanakan, ekivalen dengan $$2\sum \frac{a^2b^2}{c} + 2\sum \frac{a^3c}{b} + \sum ab^2 \geq 3(a^2b + b^2c + c^2a) + 6abc.$$ Ada yang salah hitung ga itu? Kalau tidak ada yang salah, tinggal AM-GM.


Edited by candhakkeplekkegebuk

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