The lengths of three sides of △ ABC are a, B, C respectively, and a > b > C, a, B, C are all positive integers. If the condition 1 / A + 1 / B + 1 / C = 1 is satisfied, the existence of △ ABC can be judged

The lengths of three sides of △ ABC are a, B, C respectively, and a > b > C, a, B, C are all positive integers. If the condition 1 / A + 1 / B + 1 / C = 1 is satisfied, the existence of △ ABC can be judged

Because a > b > C, a, B, C are all positive integers, the minimum value of C is 1 (1) when C = 1, 1 / A + 1 / B + 1 / C > 1 (2) when C = 2, B = 3, a = 4, 1 / A + 1 / B + 1 / C = 13 / 12 > 1, when C = 2, B = 3, a = 5, 1 / A + 1 / B + 1 / C = 31 / 30 > 1, when C = 2, B = 3, a = 6, 1 / A + 1 / B + 1 / C = 1, but 2 = 3

The positive integers a, B, C, a are known

To form a triangle, we only need to satisfy the condition: a + b > C, then a > c-b
Because ABC is a positive integer, a

It is known that the perimeter of △ ABC is 10, and the length of three sides is an integer

Let three sides be x, y, Z, then we use
x+y+z=10
x+y>z
|x-y|