Відповіді §.13 - §.14 » §.14 (4.3)

(x-3y)/y + 9y/(x-3y) = 6. (x – 1)(y + 2) = 8. Заміна (x-3y)/y = t. t + 9/t = 6. (t^2+ 9-6t)/t = 0. (t – 3)2 = 0. t = 3. (x-3y)/y = 3 ⇒ x – 3y = 3y. x = 6y. x = 6y. (x – 1)(y + 2) = 8. x = 6y. (6y – 1)(y + 2) = 8. 6y2 + 12y – y – 2 – 8 = 0. 6y2 + 11y – 10 = 0. D = 121 + 4 • 6 • 10 = 121 + 240 = 361 = 192. y1 = (-11+19)/12 = 8/12 = 2/3 y2 = (-11-19)/12 = (-30)/12 = –5/2 y = 2/3 x = 4 y = –5/2 x = –15 Відповідь: (4; 2/3); (–15; –5/2).