If the three sides of a triangle are a, B, C and satisfy A4 + B4 + C4 = a2b2 + b2c2 + c2a2, the triangle is equilateral

If the three sides of a triangle are a, B, C and satisfy A4 + B4 + C4 = a2b2 + b2c2 + c2a2, the triangle is equilateral

A 4 + B 4 + C 4 = A 2B 2 + B 2C 2 + C 2A 2, the left and right sides of a 4 + B 4 + C 4 = A 2B 2 + B 2C 2 + C 2A 2 are all × 2, which is written in the form of complete square: (a 2-B 2) 2 + (b 2-C 2) 2 + (C 2-A 2) 2 = 0, ∵ a, B, C are the three sides of the triangle respectively, ∵ a, B, C are nonnegative, ∵ a 2-B 2 = 0, B 2-C 2 = 0, C 2-A 2 = B 2, C 2 = a 2 ∵ a = b = C, the triangle is equilateral triangle