Question

Помогите, срочно, пожалуйста !!!

Answer 1

Ответ: (4,6);(6,4)

Пошаговое объяснение:

$\left \{ {{x+y = 10} \atop {\frac{1}{x} + \frac{1}{y}} = \frac{5}{12} } \right. \\ x= 10-y;\\ \frac{1}{10-y} +\frac{1}{y} = \frac{5}{12} ; \\ \frac{12y}{120y-12y^{2}} + \frac{120-12y}{120y-12y^{2}} = \frac{50y-5y^{2}}{120y-12y^{2}} \\ 12y+120-12y-50y+5y^{2} = 0 \\120-50y+5y^{2} = 0 \\y^{2}-10y+24 = 0\\D=100 - 4*24= 4\\y = 6; y =4\\\\y=6 => x=10-6=4\\ y=4 => x=10-4=6$