If the three sides of △ ABC satisfy a2-2bc = c2-2ab, then △ ABC is () A. Isosceles triangle B. right triangle C. equilateral triangle D. acute triangle

If the three sides of △ ABC satisfy a2-2bc = c2-2ab, then △ ABC is () A. Isosceles triangle B. right triangle C. equilateral triangle D. acute triangle

The equation can be transformed as: a2-2bc-c2 + 2Ab = 0, (a2-c2) + (2ab-2bc) = 0, (a + C) (A-C) + 2B (A-C) = 0, (A-C) (a + C + 2b) = 0, ∵ a, B, C are the three sides of △ ABC, ∵ a + C + 2B > 0, ∵ a-c = 0, ∵ a = c.. The triangle is isosceles triangle, so a

Three sides of triangle ABC, a, B, C satisfy a ^ 2-2bc = C ^ 2-2ab, try to judge the shape of triangle ABC

According to the meaning of the title:
a^2+2ab=c^2+2bc
Add B ^ 2 on both sides:
a^2+2ab+b^2=c^2+2bc+b^2
Then:
（a+b）^2=(b+c)^2
So: a + B = B + C
a=c;
So it's an isosceles triangle

If a, B and C are three sides of △ ABC, and a ^ 2 + 2Ab = C ^ 2 + 2BC, then what triangle is △ ABC?
Please write the reason

Both sides + B ^ 2 is (a + b) ^ 2 = (B + C) ^ 2
A = C is an isosceles triangle

If the lengths of three sides of △ ABC are a, B, C respectively and a ^ 2 + 2Ab = C ^ 2 + 2BC, then △ ABC must be______ triangle.

ABC must be an isosceles triangle
a²+2ab=c²+2bc
(a+b)²=(b+c)²
a+b=b+c
a=c