Question

Решите систему уравнений: {1/x−1/y=3/2,1/x^2−1/y^2=−3/4. В ответе укажите максимальное из чисел x, y.

Answer 1

ОДЗ: $x\neq 0,y\neq 0$

$\left \{ {{\frac{1}{x}-\frac{1}{y}=\frac{3}{2}} \atop {\frac{1}{x^2}-\frac{1}{y^2}=-\frac{3}{4}}} \right. \\ \\ \left \{ {{\frac{1}{x}-\frac{1}{y}=\frac{3}{2}} \atop {(\frac{1}{x})^2-(\frac{1}{y})^2=-\frac{3}{4}}} \right. \\ \\ \left \{ {{\frac{1}{x}-\frac{1}{y}=\frac{3}{2}} \atop {(\frac{1}{x}-\frac{1}{y})(\frac{1}{x}+\frac{1}{y})=-\frac{3}{4}}} \right. \\ \\ \left \{ {{\frac{1}{x}-\frac{1}{y}=\frac{3}{2}} \atop {\frac{3}{2}(\frac{1}{x}+\frac{1}{y})=-\frac{3}{4}}} \right.$

$\left \{ {{\frac{1}{x}-\frac{1}{y}=\frac{3}{2}} \atop {\frac{1}{x}+\frac{1}{y}=-\frac{1}{2}}} \right. \\ \\ \left \{ {{\frac{2}{x}=1} \atop {-\frac{2}{y}=2}} \right. \\ \\ \left \{ {{x=2} \atop {y=-1}} \right.$

Ответ: 2