X^2+3xy-4y^2 Разложить на множетили

1. Первый способ: x - переменная, y - параметр:

f (x) = x^2 + 3xy - 4y^2; D = (3y) ^2 + 4 * 4y^2 = 25y^2; x = (-3y ± √ (25y^2)) / 2 = (-3y ± 5y) / 2; x1 = (-3y - 5y) / 2 = - 8y/2 = - 4y; x2 = (-3y + 5y) / 2 = 2y/2 = y; f (x) = (x - x1) (x - x2); f (x) = (x + 4y) (x - y).

2. Второй способ: y - переменная, x - параметр:

g (y) = - 4y^2 + 3xy + x^2; D = (3x) ^2 + 4 * 4x^2 = 25x^2; y = (-3x ± √ (25x^2)) / (-8) = (3x ± 5x) / 8; y1 = (3x - 5x) / 8 = - 2x/8 = - x/4; y2 = (3x + 5x) / 8 = 8x/8 = x; g (y) = - 4 (y - y1) (y - y2); g (y) = - 4 (y + x/4) (y - x) = (x + 4y) (x - y).

Ответ: (x + 4y) (x - y).