\(\hept{\begin{cases}\frac{2}{x+y}+\frac{1}{x-y}=3\\\frac{1}{x+y}-\frac{3}{x-y}=1\end{cases}}\)
Đặt: \(u=\frac{1}{x+y};v=\frac{1}{x-y}\). Ta có:
\(\hept{\begin{cases}2u+v=3\\u-3v=1\end{cases}}\)
\(\hept{\begin{cases}2u+v=3\\2u-6v=2\end{cases}}\)<=> 7v=1 => \(v=\frac{1}{7};u=\frac{10}{7}\)
\(< =>\hept{\begin{cases}\frac{1}{x+y}=\frac{10}{7}\\\frac{1}{x-y}=\frac{1}{7}\end{cases}}\) <=> \(\hept{\begin{cases}10x+10y=7\\x-y=7\end{cases}}\)<=> 10(y+7)+10y=7
<=> 20y+70=7
=> \(y=-\frac{63}{20}\); \(x=\frac{77}{20}\)
a = \(\frac{1}{x+y}\)
b = \(\frac{1}{x-y}\)
=>
\(\hept{\begin{cases}2a+b=3\\a-3b=1\end{cases}}\)
<=>
\(\hept{\begin{cases}2a+b=3\\2a-6b=2\end{cases}}\)
Trừ 2 vế PT
=> 7b = 1
=> b = 1/7
=> a = 10/7
=>
\(\hept{\begin{cases}x+y=\frac{7}{10}\\x-y=7\end{cases}}\)
<=>
\(\hept{\begin{cases}x=\frac{77}{20}\\y=-\frac{63}{20}\end{cases}}\)
