Question

Giải hệ phương trình sau

\(\left\{{}\begin{matrix}\frac{2x}{x+1}+\frac{y}{y+1}=\sqrt{2}\\\frac{x}{x+1}+\frac{3y}{y+1}=-1\end{matrix}\right.\)

Answer 1

Lời giải:
HPT \(\Leftrightarrow \left\{\begin{matrix} \frac{2x}{x+1}+\frac{y}{y+1}=\sqrt{2}(1)\\ \frac{2x}{x+1}+\frac{6y}{y+1}=-2(2)\end{matrix}\right.\)

Lấy \((2)-(1)\Rightarrow \frac{5y}{y+1}=-2-\sqrt{2}\)

\(\Rightarrow 5y+(2+\sqrt{2})(y+1)=0\)\(\Rightarrow y=\frac{-2-\sqrt{2}}{7+\sqrt{2}}\)

Thay \(\frac{y}{y+1}=\frac{-2-\sqrt{2}}{5}\) vào PT (1) thu được:

\(\frac{2x}{x+1}+\frac{-2-\sqrt{2}}{5}=\sqrt{2}\)

\(\Rightarrow \frac{x}{x+1}=\frac{1+3\sqrt{2}}{5}\Rightarrow x=\frac{1+3\sqrt{2}}{4-3\sqrt{2}}\)

Vậy......