Question

\(\left\{{}\begin{matrix}x-y=10\\\dfrac{120}{x}-\dfrac{120}{y}=0,4\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}x-y=10\\\dfrac{120}{x}-\dfrac{120}{y}=0,4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=10+y\\\dfrac{120}{10+y}-\dfrac{120}{y}=0,4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=10+y\\\dfrac{120y-1200-120y}{y\left(10+y\right)}=0,4\left(2\right)\end{matrix}\right.\)

\(\left(2\right)\Leftrightarrow-3000=y^2+10y\\ \Leftrightarrow y^2+10y+3000=0\\\Leftrightarrow y^2+10y+25=-2975\\ \Leftrightarrow\left(y+5\right)^2=-2975\left(vô\:lí\right)\)

\(\Rightarrow\)pt vô nghiệm

vậy hệ phương trình đã cho vô nghiệm