Given that a, B and C are three sides of a triangle, is the value of the algebraic formula A & # 178; - 2Ab + B & # 178; - C & # 178; positive or negative, or 0? | Math enthusiast | Mathematical art

Given that a, B and C are three sides of a triangle, is the value of the algebraic formula A & # 178; - 2Ab + B & # 178; - C & # 178; positive or negative, or 0?

A-B + b-178; - c-178; = (a-b) & 178; - c-178; = (a-b + C) (a-b-c) where A-B + C = a + C-B ＞ 0 --- because the sum of the two sides of the triangle is greater than the third side, a-b-c = a - (B + C) ＜ 0 --- because the sum of the two sides of the triangle is greater than the third side

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