It is known that a, B and C are the three sides of the triangle ABC, and the positive and negative values of the square of (A-C) - B are judged

It is known that a, B and C are the three sides of the triangle ABC, and the positive and negative values of the square of (A-C) - B are judged

a-c)^2-b^2=(a+b-c)(a-b-c)
The sum of the two sides of a triangle is greater than the equal three sides
So a + b > C, a + B-C > 0
b+c>a,a-b-c

If a ^ 2 + C ^ 2 + 2B (b-a-c) = 0, judge the shape of triangle ABC

1)
(a-c)^2≥0
2)
a^2+c^2+2b(b-a-c)=0
(a^2-2ab+b^2)+(b^2-2bc+c^2)=0
(a-b)^2+(b-c)^2=0
a=b,b=c
a=b=c
The triangle ABC is an equilateral triangle

If the lengths of three sides of a triangle are three continuous natural numbers and its perimeter m satisfies 10 < m < 22, how many triangles are there

10 / 3 = 3 more than 1,
22 / 3 = 7, more than 1,
Then the side length can be 3,4,5;
4,5,6;
5,6,7;
6,7,8
There are four triangles;