Question

Помогите срочно алгебра

Answer 1

Ответ:

$1)\; \; \left \{ {{\frac{2}{x-y}+\frac{6}{x+y}=1,1} \atop {\frac{4}{x-y}-\frac{9}{x+y}=0,1}} \right.\; \; \; t=\frac{1}{x-y}\; ,\; \; p=\frac{1}{x+y}\; \; ,\; \; x\ne \pm y\; ,\; \left \{ {{2t+6p=1,1\, |\cdot (-2)} \atop {4t-9p=0,1\qquad }} \right.\oplus \\\\\\\left \{ {{2t+6p=1,1} \atop {-21p=-2,1}} \right.\; \; \left \{ {{2t=1,1}-6p \atop {p=0,1\quad }} \right.\; \; \left \{ {{2t=0,5} \atop {p=0,1}} \right.\; \; \left \{ {{t=0,25} \atop {p=0,1}} \right.$

$\left \{ {{\frac{1}{x-y}=0,25} \atop {\frac{1}{x+y}=0,1}} \right.\; \; \left \{ {{x-y=4} \atop {x+y=10}} \right.\; \; \left \{ {{2x=14} \atop {2y=6}} \right.\; \; \left \{ {{x=7} \atop {y=3}} \right.\; \; \to \; \; (7,3)$

$Otvet:\; \; (7,3)\; .$

$3)\; \; \left \{ {{x+y=8} \atop {\frac{x}{y}+\frac{y}{x} =\frac{50}{7}}} \right.\; \; \; t=\frac{x}{y}\; ,\; \; \frac{1}{t}=\frac{y}{x}\; \; ,\; \; x\ne 0\; ,y\ne 0\; \to \; \; t\ne 0\\\\t+\frac{1}{t}=\frac{50}{7}\; \; ,\; \; \frac{7t^2-50t+7}{7t}=0\; \; ,\; \; 7t^2-50t+7=0\; ,\; \; D/4=576\; ,\\\\t_1=\frac{25-24}{7}=\frac{1}{7}\; ,\; \; t_2=25+24=7\\\\\\a)\; \; \left \{ {{x+y=8} \atop {\frac{x}{y}=\frac{1}{7}}} \right.\; \; \left \{ {{\frac{y}{7}+y=8} \atop {x=\frac{y}{7}}} \right.\; \; \left \{ {{\frac{8}{7}\, y=8} \atop {x=\frac{y}{7}}} \right.\; \; \left \{ {{y=7} \atop {x=1}} \right. \; \; \to \; \; (1,7)$

$b)\; \; \left \{ {{x+y=8} \atop {\frac{x}{y}=7}} \right.\; \; \left \{ {{8y=8} \atop {x=7y}} \right.\; \; \left \{ {{y=1} \atop {x=7}} \right.\; \; \to \; \; (7,1)\\\\Otvet:\; \; (1,7)\; \; ,\; \; (7,1)\; .$