It is known that a, B and C denote the side length of △ ABC, m > 0. Proof: AA + m + BB + m > CC + M

It is known that a, B and C denote the side length of △ ABC, m > 0. Proof: AA + m + BB + m > CC + M

It is proved that: Let f (x) = XX + m (x > 0), then f '(x) = m (x + m) 2 > 0  f (x) is an increasing function on (0, + ∞). In △ ABC, if a + b > C, then a + Ba + B + m > CC + m.. CC + m < AA + B + m + Ba + B + m < AA + m + BB + m.. The original inequality holds