Question

 left { {{x+y=xy} atop { x^{2} + y^{2}=4xy }} right. [/tex]

Answer 1

2){ x^2 + y^2 = 2,5xy
{ x - y = 0,25xy

{ x^2 - 2xy + y^2 = 0,5xy
{ x - y = 0,25xy

{ (x-y)^2 = 0,5xy
{ x - y = 0,25xy

{ (0,25xy)^2 = 0,5xy
{ x - y = 0,25xy

{ 0,0625(xy)*(xy) = 0,5xy
{ x - y = 0,25xy

{ xy = 8 => x=8y
{ x - y = 0,25 * 8 => x-y = 2 =>

8y - y = 2
y^2 + 2y - 8 = 0
y1 = -4 => x1 =8/(-4) = -2
y2 = 2 => x2 = 82 = 4
Ответ: x1 = -2 и y1= -4 или
x2 = 4 и y2=2
Проверка:
x - y = 0,25xy
4 - 2 = 0,25*4*2
2 = 2

Answer 2

тоже так аналогично и первое