Question

Решите систему уравнений ху=-2; х+у=1

Answer 1

$begin{cases}xy = -2\ x + y = 1end{cases}\\ begin{cases}x(1 - x) = x - x^2 = -2\ y = 1 - xend{cases}\\ begin{cases}-x^2 + x + 2 = 0\ y = 1 - xend{cases}\\ begin{cases}-x^2 + 2x - x + 2 = x(2- x) + (2 - x) = (x + 1)(2 - x) = 0\ y = 1 - xend{cases}\\ begin{cases}x_1 = -1\ y_1 = 1 - (-1) = 2end{cases} begin{cases}x_2 = 2\ y_2 = 1 - 2 = -1end{cases}\\ mathbb{OTBET:} (-1; 2), (2; -1) .$