Question

Помогите решить систему, пожалуйста

Answer 1

$frac{1}{y} - frac{1}{x} = 3 \ 0.8 = frac{1}{x + y} \ \ frac{ x- y}{xy} = 3 \ x + y = frac{1}{0.8} \ \ x - y = 3xy \ x + y = 1.25 \ \ x = 1.25 - y \ 1.25 - y - y = 3y(1.25 - y) \ \ x = 1.25 - y \ 1.25 - 2y = 3.75y - 3 {y}^{2} \ \ x = 1.25 - y \ 3 {y}^{2} - 5.75y + 1.25 = 0 \ \ 12 {y}^{2} - 23y + 5 = 0 \ d = {b}^{2} - 4ac = 529 - 4 times 12 times 5 = 289 \ y1 = frac{23 + 17}{2 times 12} = frac{40}{24} = frac{5}{3} \ y2 = frac{23 - 17}{2 times 12} = frac{6}{24} = frac{1}{4} \ x1 = 1.25 - frac{5}{3} = frac{5}{4} - frac{5}{3} = frac{15}{12} - frac{20}{12} = - frac{5}{12} \ x2 = 1.25 - frac{1}{4} = 1$
Ответ: (-5/12; 5/3) и (1; 1/4)

Answer 2

решаем способом подстановки