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Syarat aneh

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Misalkan $a, b, c$ adalah bilangan real positif yang memenuhi $$a^b + b^c + c^a=3.$$ Buktikan bahwa $$\frac{a^3+b^3-c}{c^3}+\frac{b^3+c^3-a}{a^3}+\frac{c^3+a^3-b}{b^3} \ge a^2+b^2+c^2.$$

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