Найдите все пары целых решений уравнения

2x^2+y^2=2xy+4x

2x^2 + y^2 = 2xy + 4x

2x^2 + y^2 - 2xy = 4x

(x - y) ^2 = 4x - x^2

(x - y) ^2 = x (4 - x)

x - y = 0 4 - x = 0

y = 4 x = 4 (x; y) = (4; 4)

x - y = √ x (4 - x)

x (4 - x) = x^2

4 - x = x

2x = 4

x=2

2 * 2^2 + y^2 - 2 * 2y = 4 * 2

8 + y^2 - 4y = 8

y (y-4) = 0

y = 4 (x; y) = (2; 4)