olymmath

KöMaL 2012 A571

    The side lengths of a triangle are aa, bb, and cc. Prove that (2a+c)(2b+c)(3a+b)(3b+a)+(2b+a)(2c+a)(3b+c)(3c+b)+(2c+b)(2a+b)(3c+a)(3a+c)<52.\sqrt{\frac{(2a+c)(2b+c)}{(3a+b)(3b+a)}} + \sqrt{\frac{(2b+a)(2c+a)}{(3b+c)(3c+b)}} + \sqrt{\frac{(2c+b)(2a+b)}{(3c+a)(3a+c)}} < \frac52.

    Official text KöMaL. Quoted with source.

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