Question

решите систему уравнений
{х^2-2у^2=7
{х-у-2=0

Answer 1

Заменим х = у + 2.

(у + 2)² - 2у² = 7.

у² + 4у + 4 - 2у² = 7.

у² - 4у + 3 = 0,    D = 16 – 4*1*3 = 4,   √D = +-2.

y1 = (4 – 2)/2 = 1,

y2 = = (4 + 2)/2 = 3.

x1 = 1 + 2 = 3,

x2 = 3 + 2 = 5.

Ответ: (3; 1) и (5; 3).