Решите систему уравнений 1/x-1/y=1/12 5X-y=18

1/x - 1/y = 1/12 (x ≠ 0; y ≠ 0)

5x - y = 18

(y - x) / xy = 1/12

5x - y = 18

xy = 12 (y - x)

5x - y = 18

xy = 12 (y - x)

y = 5x - 18

x (5x - 18) = 12 (5x - 18 - x)

5x^2 - 18x = 12 (4x - 18)

5x^2 - 18x = 48x - 216

5x^2 - 18x - 48x + 216 = 0

5x^2 - 66x + 216 = 0

D = 4356 - 4320 = 36 = 6^2

x1 = (66 + 6) / 10 = 7,2

x2 = (66 - 6) / 10 = 6

x1 = 7,2

y1 = 5x1 - 18 = 18

x2 = 6

y2 = 5x2 - 18 = 12

Ответ

(7,2; 18)

(6; 12)