If the lengths of three sides of a triangle are a, B, C, and satisfy a ^ 2 + 2B ^ 2-2ab-2ac + C ^ 2 = 0, try to judge what triangle the triangle is and explain the reason

If the lengths of three sides of a triangle are a, B, C, and satisfy a ^ 2 + 2B ^ 2-2ab-2ac + C ^ 2 = 0, try to judge what triangle the triangle is and explain the reason

Equilateral triangle. The equation can be reduced to (a ^ 2-2ab + B ^ 2) + (b ^ 2-2ac + C ^ 2) = 0, that is, (a-b) ^ 2 + (B-C) ^ 2 = 0
So (a-b) ^ 2 = 0, (B-C) ^ 2 = 0, that is, a = B, B = C, so a = b = C, so the triangle is an equilateral triangle

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