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Syarat lucu

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Buktikan bahwa untuk setiap $a, b, c \in \mathbb{R}^+$ yang memenuhi $\frac{a^2+b^2+c^2}{ab+bc+ca} = \frac{ab+bc+ca+1}{2}$, dipunyai $$\sqrt{a^2+b^2+c^2} \le 1 + \frac{|a-b|+|b-c|+|c-a|}{2}.$$




ELMO SL 2013 A4


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