Question

giải hệ phương trình :\(\left\{{}\begin{matrix}x+y=75\\\frac{90}{y}-\frac{90}{x}=1\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}x+y=75\\\frac{90}{x}-\frac{90}{y}=1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=75-y\\\frac{90}{75-y}-\frac{90}{y}=1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=75-y\\90y-6750+90y=75y-y^2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=75-y\\y^2+105y-6750=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=30\\y=45\end{matrix}\right.\\\left\{{}\begin{matrix}x=225\\y=-150\end{matrix}\right.\end{matrix}\right.\)