6х^2+5mх+m^2=0х^2+2(a-b)х-4аb=0х^2=это обозначает х в квадрате

Решим квадратное уравнение:

1) 6х^2 + 5mx + m^2 = 0.

D = b^2 - 4ac = (5m)^2 - 4 * 6 * m^2 = 25m^2 - 24m^2 = m^2.

√D = √m^2 = m.

x1 = (-b + √D)/2a = (-5m + m)/12 = -4m/12 = -m/3;

x2 = (-b - √D)/2a = (-5m - m)/12 = -6m/12 = -m/2.

Ответ: х1 = -m/3, x2 = -m/2.

2) x^2 + 2 * (a - b)x - 4ab = 0;

D = b^2 - 4ac = (2 * (a - b))^2 + 4 * 4ab = 4 * (a^2 - 2ab + b^2) + 16ab = 4a^2 - 8ab + 4b^2 + 16ab = 4a^2 + 8ab + 4b^2 = 4 *(a^2 + 2ab + b^2) = 4 * (a + b)^2.

√D = √4 * (a + b)^2 = 2 * (a + b).

x1 = (-b + √D)/2a = (-2 * (a - b) + 2 * (a + b))/2 = (-2a + 2b + 2a + 2b)/2 = 4b/2 = 2b;

x2 = (-b - √D)/2a = (-2 * (a - b) - 2 * (a + b))/2 = (-2a + 2b - 2a - 2b)/2 = -4a/2 = -2a.

Ответ: х1 = 2b, x2 = -2a.