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    OlympiadHardInequalities10–12

    Nesbitt's Inequality

    Desigualdade de Nesbitt

    For positive reals aa, bb, cc, prove that ab+c+bc+a+ca+b≥32\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} \ge \frac{3}{2}.

    Add 11 to each fraction; every numerator then becomes the same quantity.

    Solution

    Step 1 of 8

    1. 1.Let s=a+b+cs = a + b + c. Adding 11 to each term,