ПОВТОРЕННЯ НАВЧАЛЬНОГО МАТЕРІАЛУ » §.2 (8.5-6)

5. y3 + x3 = 65, x – y = 3; y3 + (y + 3)3 = 65. x = y + 3. y3 + y3 + 9y2 + 27y + 27 – 65 = 0. 2y3 + 9y2 + 27y – 38 = 0. y = 1. (y – 1)(2y2 + 11y + 38) = 0. D < 0. y = 1. y = 1. x = 4, (4; 1). 6. (x+2y)/(y-x) – (y-x)/(x+2y) = 24/5, 4x + 12y = 3. Заміна (x+2y)/(y-x) = t. t – 1/t = 24/5 (5t^2- 24t-5)/5t = 0. 5t2 – 24t – 5 = 0. D = 576 + 4 • 5 • 5 = 676. t1 = (24+26)/10 = 5, t2 = –1/5 (x+2y)/(y-x) = 5. x + 2y = 5y – 5x. 6x – 3y = 0. 2x – y = 0. y = 2x. (x+2y)/(y-x) = –1/5 –5x – 10y = y – x. –4x = 11y. y = 2x 4x + 12y = 3 –4x = 11y 4x + 12y = 3 y = 2x 4x + 24x = 3 4x = –11y –11y + 12y = 3 y = 3/14 x = 3/28 x = –33/4 = –81/4 y = 3 B. (3/28; 3/14); (–81/4; 3).