Question

Решите систему уравнений с картинки:

Answer 1

$left { {{4^{(x-y)^2-1}=1} atop {5^{x+y}=125}} right. \\ 4^{(x-y)^2-1}=1\ (x-y)^2-1 = 0\\ 5^{x+y}=125\ 5^{x+y}=5^3\ x + y = 3\\ left { {{(x-y)^2-1 = 0} atop {x + y = 3}} right. \\ y = 3 - x\ (x-y)^2-1 = 0\ (x-(3-x))^2-1=0\ (2x-3)^2-1=0\ (2x-3)^2=1\\ 2x-3=1\ 2x=4\ x_1 = 2\\ 2x-3=-1\ 2x=2\ x_2=1\\ y_1 = 3-x_1=3-2=1\ y_2 = 3 - x_2 = 3-1=2$

Ответ: $(2;1), (1;2)$