In the triangle ABC, if the lengths of three sides are a, B and C respectively, and the square of a + 2Ab = the square of C + 2BC, then the triangle ABC is a triangle

In the triangle ABC, if the lengths of three sides are a, B and C respectively, and the square of a + 2Ab = the square of C + 2BC, then the triangle ABC is a triangle

(the 2 after the letter is the square, and the 2 before the letter is the double)
solution
A2+2AB=C2+2bc
a2+2ab-c2-2bc=0
a2+2ab+b2-c2-2bc-b2+0
(a+b)2-(B+C)2=0
|a+b|=|b+c|
When a + B = B + C
A = C is an isosceles triangle
When a + B = - B-C
a+c+2b=0
Because a, B, C are all greater than 0, so they do not match
Synthesis, isosceles triangle

Elden Ring Premiere

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