Question

Решить систему уравнений: x^2 + y^2 = 26 xy = -5

Answer 1

$x^2 + y^2 = 26\\ xy = -5\\ x^2 + y^2 +2xy-2xy= 26\\ xy = -5\\ (x+y)^2=26+2xy\\ (x+y)^2=26+2*(-5)\\ (x+y)^2=16\\ x+y=4\\xy=-5\\x=4-y\\4y-y^2+5=0\\y^2-4y-5=0\\y_1=-1\\y_2=5\\x_1=5\\x_2=-1\\x+y=-4\\xy=-5\\x=-4-y\\-4y-y^2+5=0\\y^2+4y-5=0\\y_3=1\\y_4=-5\\x_3=-5\\x_4=1\\(5;-1)(-1;5)(-5;1)(1;-5)$