Найдите все нецелые числа x,y,z, такие, что x+y=5xy,x+z=6xz,y+z=7yz

Ответ:

(1/5; 1/7; 1/6) && (1/6; 1/5; 1/7)

Пошаговое объяснение:

x + y = 5xy

x + z = 6xz

y + z = 7yz

_________

(5x - 1)(5y - 1) = 0

(6x - 1)(6z - 1) = 0

(7y - 1)(7z - 1) = 0

_____

1) 5x - 1 = 0

x = 1/5

=> 6z - 1 = 0 => z = 1/6

=> 7y - 1 = 0 => y = 1/7

2) 5y - 1 = 0

y = 1/5

=> 7z - 1 = 0 => z = 1/7

=> 6x - 1 = 0 => x = 1/6