Решить систему уравнений:

1/x + 1/y = 3/8

x+y=12

(1/X) + (1/y) = 3/8

(X + y) / xy = 3/8

X + y = 12

y = 12 - X

(X + 12 - X) / (x (12 - X)) = 3/8

12 / (12x - x^2) = 3/8

8•12 = 3 (12x - x^2)

8•3•4 = 3 (12 х - х^2)

32 = 12 х - х^2

Х^2 - 12 х + 32 = 0

D = 144 - 128 = 16 = 4^2

X1 = (12 + 4) : 2 = 8

X2 = (12 - 4) : 2 = 4

y = 12 - X

y1 = 12 - 8 = 4

y2 = 12 - 4 = 8

Ответ (8; 4); (4; 8)