In the isosceles triangle ABC, the opposite sides of the angles a, B and C are a, B and C respectively. It is known that a = 3, B and C are the two real roots of the equation x * + MX + 2-1 / 2m = 0 about X. find the circumference of the triangle ABC (* means square, 30 minutes)

In the isosceles triangle ABC, the opposite sides of the angles a, B and C are a, B and C respectively. It is known that a = 3, B and C are the two real roots of the equation x * + MX + 2-1 / 2m = 0 about X. find the circumference of the triangle ABC (* means square, 30 minutes)

1. B = C m ^ 2-8 + 2m = 0 solve this equation to get m = - 4, M = 2, so the original equation is x ^ 2 + 2x + 1 = 0 or x ^ 2-4x + 4, then B = C = - 1 (rounding off), B = C = 2, because B + C > A, so it holds, C = 7
2. If a = B or a = C, then x = 3 is the solution of the original equation, 9 + 3M + 2-1 / 2m = 0, M = - 22 / 5, then the original equation is x ^ 2-22 / 5x + 2 + 11 / 5 = 0
X = 7 / 5, because 6 > x, C = 37 / 5