Question

Пжжжжж!!!!!!!!!!!!!!!!!!!!​

Answer 1

$\left\{\begin{array}{l}\dfrac{1}{x+y}+\dfrac{1}{x-y}=17\, |\cdot 6\\\dfrac{6}{x+y}+\dfrac{10}{x-y}=138\end{array}\right\ \ \left\{\begin{array}{l}\dfrac{6}{x+y}+\dfrac{6}{x-y}=102\\\dfrac{6}{x+y}+\dfrac{6}{x-y}+\dfrac{4}{x-y}=138\end{array}\right\\\\\\\left\{\begin{array}{l}\dfrac{1}{x+y}+\dfrac{1}{x-y}=17\\102+\dfrac{4}{x-y}=138\end{array}\right\ \ \left\{\begin{array}{l}\dfrac{1}{x+y}+\dfrac{1}{x-y}=17\\\dfrac{4}{x-y}=36\end{array}\right$

$\left\{\begin{array}{l}\dfrac{1}{x+y}+\dfrac{1}{x-y}=17\\x-y=\dfrac{1}{9}\end{array}\right\ \ \left\{\begin{array}{l}\dfrac{1}{x+y}+\dfrac{1}{x-y}=17\\x=y+\dfrac{1}{9}\end{array}\right\ \ \left\{\begin{array}{l}\dfrac{1}{2y+\frac{1}{9}}+\dfrac{1}{\frac{1}{9}}=17\\x=y+\dfrac{1}{9}\end{array}\right$

$\left\{\begin{array}{l}\dfrac{9}{18y+1}+9=17\\x=y+\dfrac{1}{9}\end{array}\right\ \ \left\{\begin{array}{l}\dfrac{9}{18y+1}=8\\x=y+\dfrac{1}{9}\end{array}\right\ \ \left\{\begin{array}{l}18y+1=\dfrac{9}{8}\\x=y+\dfrac{1}{9}\end{array}\right\ \ \left\{\begin{array}{l}18y=\dfrac{1}{8}\\x=y+\dfrac{1}{9}\end{array}\right$

$\left\{\begin{array}{l}y=\dfrac{1}{144}\\x=y+\dfrac{1}{9}\end{array}\right\ \ \left\{\begin{array}{l}y=\dfrac{1}{144}\\\, x=\dfrac{1}{144}+\dfrac{1}{9}\end{array}\right\ \ \left\{\begin{array}{l}y=\dfrac{1}{144}\\\, x=\dfrac{17}{144}\end{array}\right\\\\\\Otvet:\ \ \Big(\, \dfrac{17}{144}\ ;\ \dfrac{1}{144}\, \Big)\ .$

Answer 2

$\left \{ {{\frac{1}{x+y} +\frac{1}{x-y} =17} \atop {\frac{6}{x+y} +\frac{10}{x-y} =138}} \right.$

Замена:

$\frac{1}{x+y} =a;$      $\frac{1}{x-y} =b$

$\left \{ {{a+b=17} \atop {6a+10b=138}} \right.$

$\left \{ {{a=17-b} \atop {6a+10b=138}} \right.$

$6*(17-b)+10b=138$

$102-6b+10b=138$

     $4b=138-102$

       $b=36:4$

      $b=9$

$a=17-9=8$

      $a=8$

Обратная замена:

$\left \{ {{\frac{1}{x+y} =8} \atop {\frac{1}{x-y} =9}} \right.$

$\left \{ {{8x+8y=1} \atop {9x-9y=1}} \right.$

$\left \{ {{9*8x+9*8y=9*1} \atop {8*9x-8*9y=8*1}} \right.$

$\left \{ {{72x+72y=9} \atop {72x-72y=8}} \right.$

1)   Сложим эти уравнения:

$72x+72y+72x-72y=9+8$

$144x=17$

      $x=\frac{17}{144}$

2)  Вычтем из первого уравнения второе:

$\left \{ {{72x+72y=9} \atop {72x-72y=8}} \right.$

$72x+72y-72x+72y=9-8$

$144y=1$

      $y=\frac{1}{144}$

Ответ:   $\left \{ {{x= \frac{17}{144} } \atop {y=\frac{1}{144} }} \right.$