Question

Системa уравнений:
x/y-y/x=5/6
x^2-y^2=5

Answer 1

$x \neq 0\ ; y\neq 0$
$\left \{ {{ \frac{x}{y}- \frac{y}{x}= \frac{5}{6} } \atop {x^2-y^2=5}} \right. \\ \left \{ {{\frac{x^2-y^2}{xy} =\frac{5}{6}} \atop {x^2-y^2=5}} \right. \\ \left \{ {{ \frac{5}{xy}= \frac{5}{6} } \atop {x^2-y^2=5}} \right. \\ \left \{ {{xy=6} \atop {x^2-y^2=5}} \right. \\y= \frac{6}{x} \\x^2- \frac{36}{x^2} =5 \\x^4-5x^2-36=0 \\u=x^2;\ u \geq 0 \\u^2-5u-36=0 \\D=25+144=169=13^2 \\u_1= \frac{5+13}{2}=9 \\u_2= \frac{5-13}{2} \ \textless \ 0 \\x^2=9 \\x_1=3 \\x_2=-3 \\y_1= \frac{6}{3}=2 \\y_2= \frac{6}{-3} =-2$
Ответ: (3;2) и (-3;-2)