Question

giải hệ phương trình

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

Answer 1

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

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

\(\Leftrightarrow\left\{{}\begin{matrix}-2a+b=1\\3a+\frac{1}{b}=-3\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}-6a+3b=3\\6a+\frac{2}{b}=-6\end{matrix}\right.\)

\(\Rightarrow3b+\frac{2}{b}=-3\)

\(\Leftrightarrow3b^2+3b+2=0\)(Xét delta thấy nó <0 nên pt vô nghiệm)

Pt vô nghiệm nên Hệ Pt vô nghiệm