Question

Решите систему , 1/x + 1/y =12 - первое уравнение системы 1/x - 1/y = 0,45 * 1/x+y - второе уравнение системы

Answer 1

$x \neq 0;y \neq 0\\ \left \{ { \frac{x+y}{xy} =12} \atop { \frac{y-x}{xy} = \frac{0,45}{x+y} }} \right. \\ \left \{ {{x+y=12xy} \atop {\frac{y-x}{xy} = \frac{0,45}{12xy} }} \right. \\ \left \{ {{y+x=12xy} \atop {y-x = \frac{0,45}{12} }} \right. \\ \left \{ {{y = \frac{0,45}{12}+x} \atop {\frac{0,45}{12}+x+x=12x(\frac{0,45}{12}+x)}} \right. \\ \left \{ {{y = \frac{0,45}{12}+x} \atop {\frac{0,45}{12}+2x=0,45x+12x^2}} \right. \\ \left \{ {{y = \frac{0,45}{12}+x} \atop {12x^2-1,55x-\frac{0,45}{12}}=0} \right.$
$D=1,55^2+4*0,45=2,05^2\\x_1=- \frac{1}{48} ; x_2= \frac{3}{20} \\y_1= \frac{1}{60} ;y_2= \frac{3}{16} \\(- \frac{1}{48} ;\frac{1}{60}) , (\frac{3}{20} ;\frac{3}{16})$