Question

Решите систему уравнений 1/х-1/у=1/2 ху=-16

Answer 1

$\left \{ {{\frac{1}{x} -\frac{1}{y}=\frac{1}{2}} \atop {xy=-16}} \right.\\\\\left \{ {{\frac{y-x}{xy} =\frac{1}{2} } \atop {xy=-16}} \right.\\\\\left \{ {{\frac{y-x}{-16}=\frac{1}{2}} \atop {xy=-16}} \right.\\\\\left \{ {{y-x=-8} \atop {xy=-16}} \right.\\\\\left \{ {{y=x-8} \atop {x(x-8)=-16}} \right.\\\\\left \{ {{y=x-8} \atop {x^{2}-8x+16=0 }} \right.\\\\\left \{ {{y=x-8} \atop {(x-4)^{2}=0 }} \right.\\\\\left \{ {{y=x-8} \atop {x-4=0}} \right.$

$\left \{ {{y=4-8} \atop {x=4}} \right.\\\\\left \{ {{x=4} \atop {y=-4}} \right.$

Ответ : (4 ; - 4)