Question

Решите пожалуйста 20.51

Answer 1

$left { {{frac{3}{2x+y}+frac{1}{2x-y}=frac{2}{5}} atop {frac{7}{2x+y}+frac{2}{2x-y}=frac{3}{5}}} right.$

Пусть $2x+y=a, 2x-y=b, aneq 0,bneq 0$

$left { {{frac{3}{a}+frac{1}{b}=frac{2}{5}} atop {frac{7}{a}+frac{2}{b}=frac{3}{5}}} right. \ \ left { {{-frac{6}{a}-frac{2}{b}=-frac{4}{5}} atop {frac{7}{a}+frac{2}{b}=frac{3}{5}}} right. \ \ left { {{frac{1}{a}=-frac{1}{5}} atop {7cdot(-frac{1}{5})+frac{2}{b}=frac{3}{5}}} right. \ \ left { {{a=-5} atop {-frac{7}{5}+frac{2}{b}=frac{3}{5}}} right. \ \ left { {{a=-5} atop {frac{2}{b}=frac{10}{5}}} right.$

$left { {{a=-5} atop {frac{2}{b}=2}} right.\ \ left { {{a=-5} atop {b=1}} right.$

Возвращаемся к исходным переменным:

$left { {{2x+y=-5} atop {2x-y=1}} right. \ \ left { {{4x=-4} atop {2y=-6}} right. \ \ left { {{x=-1} atop {y=-3}} right.$

Ответ: $(-1;-3)$