Question

1/(x+y) + 1/(x-y)= 5
3/(x+y)+ 1/(x-y)=7
решите систему уравнений

Answer 1

Сделаем замену :

$\frac{1}{x+y}=m\\\\\frac{1}{x-y}=n\\\\-\left \{ {{m+n=5} \atop {3m+n=7}} \right.\\ -------\\2m=2\\m=1\\n=5-m=5-1=4\\\\\frac{1}{x+y}=1\\\\x+y=1\\\\\frac{1}{x-y}=4\\\\x-y=0,25\\\\+\left \{ {{x+y=1} \atop {x-y=0,25}} \right.\\2x=1,25\\\\x=0,625\\\\y=1-0,625=0,375\\\\Otvet:\boxed{(0,625;0,375)}$