Question

решить систему уравнения
x^2-y=8;
x-y=6

Answer 1

Ответ: (2; -4) ; (-1; -7)

${x}^{2} - y = 8 \\ x = 6 + y \\ \\ {(6 + y)}^{2} - y = 8 \\ 36 + 12y + {y}^{2} - y - 8 = 0 \\ {y}^{2} + 11y + 28 = 0 \\ D = {b}^{2} - 4ac = {11}^{2} - 4 \times 1 \times 28 = 121 - 112 = 9 \\ \sqrt{D} = \sqrt{9} = 3 \\ y1 = \frac{ - b + \sqrt{D} }{2a} = \frac{ - 11 + 3}{2} = \frac{ - 8}{2} = - 4 \\ y2 = \frac{ - b - \sqrt{D} }{2a} = \frac{ - 11 - 3}{2} = - \frac{ - 14}{2} = - 7 \\ y1 = - 4 \: ⇒ \: x1 = 2 \\ y2 = - 7 \: ⇒ \: x2 = - 1$