If the three sides of a triangle a B C satisfy a Λ 2b-a Λ 2c-ab Λ 2 + AC Λ 2 + B Λ 2C_ BC ∧ 2 = 0, judge the shape of triangle

If the three sides of a triangle a B C satisfy a Λ 2b-a Λ 2c-ab Λ 2 + AC Λ 2 + B Λ 2C_ BC ∧ 2 = 0, judge the shape of triangle

By a ^ 2b-a ^ 2c-ab ^ 2 + AC ^ 2 + B ^ 2c-bc ^ 2 = 0 = > A ^ 2 (B-C) - A (b ^ 2-C ^ 2) + BC (B-C) = 0 = > A ^ 2 (B-C) - A (B + C) (B-C) + BC (B-C) = 0 = > (B-C) (a ^ 2-ab-ac + BC) = 0 = > (B-C) (a (a-b) - C (a-b)) = 0 = > (B-C) (a-b) (A-C) = 0 = > b = C or a = B or a = C, the triangular ABC is an isosceles triangle