Question

Tìm \(x,y\in Z\) sao cho : \(\frac{2}{x}+\frac{3}{y}=5\)

Answer 1

bai truoc bi sai nha

\(\frac{2}{x}+\frac{3}{y}=5\Leftrightarrow\frac{2y+3x}{xy}=5\Leftrightarrow2y+3x=5xy\Leftrightarrow\left\{{}\begin{matrix}3x⋮y\\2y⋮x\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}6x⋮y\\6y⋮x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x=yk\\6y=xn\end{matrix}\right.\left(n;k\in Z\right)\Leftrightarrow\left\{{}\begin{matrix}x=\frac{yk}{6}\\y=\frac{xn}{6}\end{matrix}\right.\)

\(x=\frac{yk}{6}\Leftrightarrow x=\frac{xnk}{6}\Leftrightarrow nk=6=1.6=2.3=3.2=6.1=\left(-2\right).\left(-3\right)=\left(-3\right).\left(-2\right)=\left(-1\right).\left(-6\right)=\left(-6\right).\left(-1\right)\)

sau do xet 8TH nay

Answer 2

\(\frac{2}{x}+\frac{3}{y}=5\Leftrightarrow\frac{2y+3x}{xy}=5\Leftrightarrow5xy=2y+3x\)

\(\Leftrightarrow\left\{{}\begin{matrix}x⋮y\\y⋮x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-y\\x=y\end{matrix}\right.\)

\(+,x=y\Rightarrow\frac{2}{x}+\frac{3}{x}=\frac{5}{x}=5\Rightarrow x=y=1\)

\(+,x=-y\Rightarrow\frac{2}{x}+\frac{3}{-x}=5\Rightarrow\frac{2}{x}+\frac{-3}{x}=5\Rightarrow\frac{-1}{x}=5\Rightarrow x=-\frac{1}{5}\left(\text{vo li}\right)\)

vay x=y=1